British number one Johanna Konta recovered from a slow start to reach the quarter-finals of the Shenzhen Open in China.
The world number 10 lost the first set to American Vania King, ranked 77th, and trailed 3-1 in the second.
But she regained her composure to beat her opponent 1-6 6-3 6-2.
Konta, who is the third seed at the event, will face either Kristyna Pliskova or qualifier Kai-Chen Chang in the last eight.
In the Hopman Cup Great Britain are doing badly losing all six matches played in the first two rounds of the round robin stage. Dan Evans losing both his is straight sets, both doubles in straight sets, Heather Watson losing both here by two sets to one. The last of the round robin matches are tomorrow but Great Britain cannot get to the finals.
Not a good start to the year for Heather Watson. She's now at the same age (their birthdays are 2 days apart) as Johanna Konta was a year ago and 2017 has to be a key year as to if she is able to get into the top 30.
British number one Johanna Konta continued her good start to 2017 by reaching the semi-finals of the Shenzhen Open in China.
The world number 10 defeated Kristyna Pliskova of the Czech Republic, ranked 60th, 6-4 6-7 (11-13) 6-3.
Her next opponent will be another Czech, Katerina Siniakova, who beat Serbian Nina Stojanovic 6-3 6-4.
Konta is now the highest-ranked player left in the event after world number three Agnieszka Radwanska's exit.
The Polish top seed was beaten 6-2 3-6 6-0 by American world number 39 Alison Riske, who will face Camila Giorgi of Italy in the last four.
Konta looked in control early on against her opponent - the twin sister of world number six Karolina Pliskova - as she took the first set with a single break of serve.
Neither player could force a break point in the second set and in the resulting tie-break Konta wasted two match points before the big-serving Pliskova levelled the match on her fifth set point.
But Konta stayed firm in the final set, claiming the break and reaching the semi-final on her fifth match point.
"I am very happy to have extended my stay here," she said.
"She is one of the best servers on tour so I knew I was going to have a hard time on her service games. I was very happy I was able to get that break in the third and see it out in the end."
Johanna Konta suffered a shock defeat in the Shenzhen Open semi-finals, losing in three sets to world number 52 Katerina Siniakova.
The British number one lost 1-6 6-4 6-4 to her 20-year-old opponent in China.
Third seed Konta - the world number 10 - was the highest-ranked player remaining in the draw.
"I'm happy I got to play four really great matches in the first week of the season. I feel very fortunate to have gotten that time on court," said Konta.
The Briton won the opening set in just 22 minutes and led 4-2 in the decider, but Siniakova won four successive games to reach her third WTA final.
Konta said: "I think she definitely started slower, and me, quite well. But all credit to her, she really raised her level in the next two sets.
"She was going for every single shot and played quite freely, so it was a difficult match for me to do what I would have liked."
Johanna Konta, Heather Watson, Laura Robson and Jocelyn Rae have been named in the British Fed Cup squad for February's matches in Estonia.
It is the first team to be picked by new captain Anne Keothavong.
Two changes can be made before the final selection deadline on 7 February.
"In Johanna Konta we are lucky to have a player who is at the very top of the game right now," said Keothavong of the British number one, who broke into the world's top 10 last year.
"Along with Jo, we have fantastic experience in Heather and Laura, with nearly 40 Fed Cup rubbers between them, and Joss Rae gives us a strong doubles option."
Robson has been chosen ahead of Tara Moore who, at 165 in the world, is currently ranked higher, while Naomi Broady has not made herself available for selection.
The round-robin pool matches in the Euro/Africa group will take place between 8 and 10 February, with the winners competing in promotion play-offs on 11 February.
Two nations will advance to the World Group II play-offs on 22-23 April.
British number one Johanna Konta reached the last eight of the Sydney International with a 6-1 6-3 victory over Australian Daria Gavrilova.
The 25-year-old broke the world number 25 in the opening game and dropped only four points on serve in the first set.
The world number 10 wasted four match points on her own serve in the eighth game of the second set, but broke Gavrilova in the ninth to seal victory.
Konta will play Russian world number 26 Daria Kasatkina in the quarter-finals.
The 19-year-old beat world number one Angelique Kerber earlier. Third seed Dominika Cibulkova and fifth seed Svetlana Kuznetsova were also beaten on Tuesday.
Konta said: "It's such a strong tournament, such depth. I know going into every single match that it's going to be a tough one and I'm just going to have to, first and foremost, take care of things my end."
British number one Johanna Konta reached the Sydney International semi-finals.
World number 10 Konta triumphed 6-3 7-5 against Russian 19-year-old Daria Kasatkina, who beat world number one Angelique Kerber in the previous round.
The 25-year-old will face Canadian Eugenie Bouchard in the last four.
Great Britain's Laura Robson lost in straight sets in the first round of qualifying at the Australian Open.
The 22-year-old former British number one, ranked 222 in the world after three years of wrist problems, lost 6-2 6-4 to Amandine Hesse of France.
"I had a weird thought just before I went on court - I thought last time I played a match here I then didn't play for 18 months," she said.
"It maybe wasn't the best thing to happen before a match and I felt flat."
She added: "I just never got going, it felt like my feet were stuck in mud."
The left-hander, who reached the main draw of the US Open in August, has now lost seven consecutive matches and will return to Europe to play on the second-tier Challenger tour.
"It doesn't take much to change it around," the former Wimbledon junior champion said.
"Before the US Open I won one match and didn't have much confidence and then as soon as you win two matches, you think 'maybe I'm not as bad as I thought'."
Robson's compatriot Tara Moore, 24, also lost to end British interest in the qualifying section of the women's draw.
Moore, the world number 165, was beaten 6-7 (7-2) 6-3 6-1 by Hungary's Dalma Galfi.
The first Grand Slam tournament of the year starts in Melbourne on Monday. Johanna Konta, Heather Watson and Naomi Broady go straight in the main draw to be made tomorrow.
British number one Johanna Konta reached the final of the Sydney International with a 6-2 6-2 win over Eugenie Bouchard.
Konta, the world number 10, was in impressive form as she beat the Canadian in one hour and eight minutes.
The first set was tied at 2-2 before Konta reeled off seven games in a row on the way to victory.
She will now play world number three Agnieszka Radwanska, who beat Barbora Strycova 6-1 6-2, in Friday's final.
Konta, who has one tour title to her name, has played Radwanska twice before and lost each time.
The most recent of those defeats came in the China Open final last October.
Draw made for the Australian Open:
Kirsten Flipkens against Johanna Konta. Kirsten Flipkens has been a Wimbledon semi-finalist but Johanna Konta must be favourite to win.
Heather Watson against Sam Stosur, the 18th seed. Sam Stosur doesn't do that well at home in the Australian Open so Heather Watson could win this one.
Daria Gavrilova, the 22nd seed, against Naomi Broady.
British number one Johanna Konta won the Sydney International on Friday with an impressive 6-4 6-2 victory over Agnieszka Radwanska in Australia.
World number 10 Konta broke her Polish opponent in the third game and hit 18 winners to five in the first set.
The 25-year-old dominated world number three Radwanska with some stunning returns and powerful hitting, and she convincingly won the second set.
Konta finished the match off with an ace to claim her second WTA tour title.
The Briton's display will also give her confidence going into the year's first Grand Slam when she starts her Australian Open challenge against Kirsten Flipkens next week.
She reached the semi-finals at Melbourne Park in 2016, losing to eventual winner Angelique Kerber.
Konta had been beaten in both her previous matches against Radwanska, including the China Open final, and lost the first six points of the match.
But, from 0-30 down on her own serve in the second game, Konta quickly turned the match around and took her third break point in the third game of match to seize the initiative.
Her highlights in the first set included a second serve ace and some heavy hitting before a service game to love to wrap it up.
Konta twice broke Radwanska at the start of the second set to go 4-0 up and she finished off proceedings with her seventh ace to secure victory in one hour and 21 minutes.
BBC tennis correspondent Russell Fuller
This was a breathtaking performance by Konta - she was very aggressive from the baseline and served superbly.
The 25-year-old has given plenty of notice of her talent over the past 18 months, but this was a display which marked her out as a potential winner of the Australian Open - although her draw is very tough and she has played nine matches on two continents in the first two weeks of the season.
Konta will equal her career high ranking of ninth on Monday and no player has accumulated more ranking points than she has so far this year.
British women's number one Konta beat Kirsten Flipkens 7-5 6-2.
Konta last year became the first British woman to reach an Australian Open semi-final since Sue Barker in 1977, and the first to reach the last four at any Grand Slam since Jo Durie at the 1983 US Open.
Konta, who won the Sydney warm-up tournament last week, will next face Naomi Osaka after the 19-year-old Japanese beat Luksika Kumkhum.
Flipkens, ranked 70 in the world, began well but Konta, considered a serious contender to win her first Grand Slam title, soon improved.
The 25-year-old was serving for the opening set at 5-4 but Flipkens broke back after a 10-minute game which saw both players miss several good chances.
Konta, named the WTA's most improved player of 2016, responded by breaking Flipkens again and then held her serve to love to take the opening set after 51 minutes.
The Briton dominated the second set, securing two breaks of serve, to wrap up victory.
"It was incredibly tricky. She has the kind of game that can trouble any player," said Konta.
"I tried to play myself in to the match and I'm happy to be through. A lot has happened in the last year and I'm just enjoying playing and trying to get better every day."
Heather Watson overcame Australia's 18th seed Sam Stosur 6-3 3-6 6-0.
British number two Watson, who has lost in the first round in her past three appearances at the Australian Open, was broken early by home favourite Stosur.
However, former US Open champion Stosur could not keep any consistency and Watson eventually secured a place in the second round after two hours and 15 minutes.
"There were some very long games and I had a slow start in both of the first two sets - in the third I wanted to make her work," said Watson, 24.
"Sam's a great player - she's beaten me both times before. I felt I prepared really well and felt fit in that third set."
Watson, ranked 81, will face American Jennifer Brady or Belgian Maryna Zanevska in her next match.
Heather Watson's opponent in the second round is Jennifer Brady who is ranked 116. That match and Johanna Konta's look as if they will be on Thursday. Heather is playing doubles with Naomi Broady and their first round match is tomorrow. No news yet on the mixed doubles so I don't know if Heather and Henri Kontinen will be involved in that following their triumph at last year's Wimbledon.
Heather Watson, 24, but was unable to clinch victory against the world number 116, Jennifer Brady.
The British number two, ranked 35 places higher than Brady, took the first set without any fuss and was on course to win in straight sets, only to be broken when serving at 5-4.
She lost the tie-break and from there her 21-year-old opponent grew in confidence during a final set which lasted 86 minutes.
Watson had two break points in the fourth game, five more in the fifth, which she led 40-0 but failed to see out, and two more in the eighth but Brady survived them all.
At 6-5, the Briton had three match points on Brady's serve but squandered all of them as the American levelled.
Watson had her fourth and fifth match points at 8-7 but two strong serves ensured Brady again held on.
Watson served a double fault to hand Brady a 9-8 lead and although the Briton saved two match points on the American's serve she could not stop a third as her opponent sealed victory.
Ninth seed Johanna Konta, 25, produced a confident display to beat 19-year-old Naomi Osaka of Japan 6-3 6-2.
Konta, who will now face Denmark's 17th seed Caroline Wozniacki on Saturday, faced one of the most promising players in the women's game.
The big-serving Osaka, ranked 48th, had a chance to break Konta in the eighth game but missed a forehand and then looked on helplessly as the Briton fired down two aces to hold serve.
Konta took advantage of her opponent's loss of focus to break to love and then served out the opening set in clinical fashion.
The Briton dominated the second set to secure her 10th win of 2017.
"I love playing on these amazing courts and I'm looking forward to staying here as long as possible," she said.
Former Fed Cup coach Judy Murray on Radio 5 live sports extra
Johanna Konta is looking every bit the contender. She has one of the best serves in the women's game, moves well, defends much better and plays well off both sides.
She looks confident, determined and focused. She has a strong team in her corner and is in a very good position to go far in this competition.
Britain's Johanna Konta saw off former world number one Caroline Wozniacki with a stunning display to reach the fourth round of the Australian Open.
Konta, seeded ninth, won nine games in a row on her way to beating the Danish 17th seed 6-3 6-1 in 75 minutes.
It was an eighth successive victory for the Briton, who won the title in Sydney in the build-up to Melbourne.
Konta, 25, will face Ekaterina Makarova next after the Russian upset sixth seed Dominika Cibulkova 6-2 6-7 (3-7) 6-3.
"We played in the fourth round here last year and I think it was 8-6 in the third, so I am expecting a battle," Konta said.
"It will be tough, just like against anyone in any match, you don't have any easy matches any more."
Six-time champion Serena Williams - a potential quarter-final opponent for Konta - earlier beat fellow American Nicole Gibbs 6-1 6-3.
"I think if she keeps playing like this, then she has good chances against Serena," Wozniacki said of Konta.
"Serena has won so many Grand Slams and she's been in tough positions. But I think Johanna is playing on a very high level right now."
After a tight start to the contest on Margaret Court Arena, Konta took control midway through the first set and powered away from Wozniacki.
The British number one's consistent aggression on serve, return and off the ground left the Dane struggling to find an answer.
A thumping drive volley gave Konta the first break of serve in game seven and she got the better of the Wozniacki serve once again to clinch the set.
A bewildered Wozniacki double-faulted twice to fall behind in the second set and in the end she did well to get on the scoreboard at all after going 5-0 down.
There was the odd sign of nerves from Konta as she closed in on victory but after double-faulting on her first match point, she converted the second to end the day with 31 winners to Wozniacki's six.
"I definitely played at a high level today," Konta said.
"Caroline really makes you work for it and doesn't give you anything so I am happy with my level.
"I knew it would be incredibly tough and I wanted to assert myself from the get go and play the match I wanted to play. What an amazing crowd, you guys were incredible."
Britain's Johanna Konta produced another terrific performance to beat Russian Ekaterina Makarova and set up an Australian Open quarter-final against Serena Williams.
Konta, seeded ninth, saw off 30th seed Makarova 6-1 6-4 to reach the last eight without dropping a set.
The Briton, 25, reached her first Grand Slam semi-final in Melbourne last year.
Second seed Williams overcame stern resistance from Czech 16th seed Barbora Strycova to win 7-5 6-4.
Asked about facing the 22-time Grand Slam champion for the first time, Konta said: "Believe it or not that's an incredible experience for me.
"She's one of the few players still playing who I watched growing up. As a young girl wanting to be a professional tennis player, it's an incredible honour and I can't wait to play on court with her.
"Once out on court, against anyone, anyone is out there to compete. Hopefully I'll come off as the winner.
"In terms of enjoying the opportunity and the competition, I will cherish every minute out there."
Konta arrived in Melbourne having won her second WTA title in Sydney, the city in which she was born, and Monday's victory over Makarova made it nine matches and 18 sets in a row.
She had needed three hours to beat Makarova at the same stage of the 2016 tournament, but 12 months on the Briton has established herself as a true Grand Slam contender.
Dominant in every aspect of the game, she raced through the first set in just 24 minutes, winning 78% of points on her serve and, more impressively, 62% on the Makarova serve.
Her constant aggression left the flat-hitting Makarova struggling to get a racquet on the ball much of the time.
Konta's level dropped in the second set as her first serve deserted her briefly, allowing Makarova to build a 4-1 lead, but the Briton came storming back with five games in a row - closing out the match superbly from 0-40 with two aces along the way.
"I think I came out definitely playing at a higher level than she did but she really put herself back into that match and made it difficult for me," said Konta.
"The way she pulled away in the second set, I don't feel like I did much wrong, she started playing some incredible tennis."
Williams' coach, Patrick Mouratoglou, picked Konta earlier in the week as a leading threat to his player, and the theory will now be tested when they meet for the first time.
Six-time champion Serena Williams outplayed Britain's Johanna Konta to reach the Australian Open semi-finals.
The American, 35, won 6-2 6-3 and will next play unseeded Croat Mirjana Lucic-Baroni, who beat fifth seed Czech Karolina Pliskova 6-4 3-6 6-4.
Konta, seeded ninth, went into the quarter-final on a nine-match and 18-set winning streak but came up short in her first meeting with Williams.
Williams is now two wins from claiming an Open-era record 23rd major title.
"Johanna Konta has been playing so well," said the second seed.
"I was in the locker room watching her clean up her matches. She is a future champion here for sure, so I am pleased to get through this.
"I got a little frustrated with my serve, but I told myself 'don't get Babyrena' [Williams' angry alter-ego] and focused on enjoying myself out here. Today I felt I can do this, it is such a great opportunity for me."
Konta described facing Williams as the "best experience of my life".
In a match of big hitting and small margins, it was Williams who established an early control she would not relinquish.
The American's usually dominant first serve faltered as she made just 45%, but she returned brilliantly to break the Konta serve - the best on tour this season going into the match - four times.
Konta had the first chance but went long with a backhand on break point at 1-1, then found her second serve under greater pressure than at any stage of the tournament so far.
Williams looked razor sharp on return, with two thumping forehand winners setting the American on the way to a 3-1 lead.
More heavy blows brought a second break, and with it the set, in game eight to end a run of 18 straight sets for Konta stretching back to her warm-up win in Sydney.
Konta showed why she had been seen as a real threat by recovering from 0-40 early in the second set and then breaking to lead 3-1, but a loose game handed the advantage back and Williams raced through five straight games to victory.
Great Britain's Fed Cup captain Anne Keothavong says they can emulate the men's Davis Cup team and "put women's tennis on the map in this country".
They begin their campaign in Estonia on Wednesday in the Europe/Africa Zone.
Johanna Konta, the first British woman to reach the world's top 10 in 32 years, Heather Watson and Laura Robson are all available for the first time.
"Hopefully Jo's success and the way she goes about it will inspire the other girls," said Keothavong, 33.
British number one Konta, 25, reached the quarter-finals of the Australian Open before a nine-match winning streak - which included victory at the Sydney International - was ended by Serena Williams.
"They can definitely learn a lot from her," added Keothavong. "For the first time ever we've got a top-10 player so that in itself gives the team a different feel.
"We all know what she's capable of, but Laura and Heather have also had big wins and they're still very young."
World number one Andy Murray inspired Great Britain to Davis Cup victory in 2015 - but his mother, Judy Murray, quit as Fed Cup captain last year frustrated at the competition's format and Britain's failure to progress.
Keothavong's side will play a round-robin in Tallinn and need to win three or four matches to earn the chance of a play-off spot in World Group II, the Fed Cup's second tier.
"The format doesn't lend itself to anything - but it is what it is and we have to accept that," added Keothavong, who played in 39 ties for Great Britain.
"There's only eight teams in the Fed Cup World Group whereas Davis Cup has 16 so, with the format, it will take us a few years to get there.
"But we can certainly put women's tennis on the map in this country."
Great Britain is in Pool C along with Turkey, Latvia and Portugal. Each country plays 2 singles followed by a doubles against each of the other countries. The winner of Pool C will play the winner of Pool B on the last day to progress to the World Group II playoffs in April.
So GB will need to win 2 or 3 of the rounds against Turkey, Latvia and Portugal and win the round on the last day.
GB do have a fair chance with Latvia being the main challenger.
Johanna Konta has beaten Michelle Larcher de Brito 6-2, 6-4.
Next is the doubles with Jocelyn Rae and Laura Robson against Michelle Larcher de Brito and Ines Murta. It's not a dead rubber as if two countries are tied at the top of the pool, the number of matches won decides the top spot.
GB off to a good start against Latvia with Heather Watson beating Diana Marcinkevic, who is ranked 307, 6-3, 6-0 in 61 minutes.
The next match is the key one with Johanna Konta against Jelena Ostapenko who is ranked 35. The doubles match is also close as the two Latvian players (Marcinkevic and Ostapenko again) have better rankings than Jocelyn Rae and Laura Robson but will have already played today.
And Johanna Konta has beaten Jelena Ostapenko 6-2, 6-3.
I think that if GB win the doubles then Latvia cannot top the pool. Assuming that Turkey win all 3 matches against Portugal then GB would only need to win one of their matches against Turkey tomorrow to top the pool.
The Turkey/Portugal matches have been completed. The Pool C table now shows:
Great Britain 2 wins 0 losses and rubbers 6 won 0 lost
Turkey 1 win 1 loss and rubbers 3 won and 3 lost
Latvia 1 win 1 loss and rubbers 2 won and 4 lost
Portugal 0 wins 2 losses and rubbers 1 won and 5 lost
So GB just need to win one match tomorrow against Turkey to ensure they get to Saturday's matches. The opponents om Saturday will be the winner of tomorrow's matches between Croatia and Hungary.
Just looked at the regulations and found that the winner of each round of matches gets 1 point. Where two countries have the same number of points, the results between those two countries are then taken into account. That means that GB has to win 2 of the 3 matches against Turkey today rather than what I had thought was which was the number of games won.
Johanna Konta has lost the first set against Cagla Buyukakcay though has broken serve in the second.
Johanna Konta has beaten Cagla Buykakcay 5-7, 6-4, 6-3 after 2 hours 37 minutes.
That means that GB goes through to tomorrow. Their opponents will be the winner of the doubles match between Croatia and Hungary as both countries won of the the two singles matches this morning.
GB v Croatia is underway. First match is Heather Watson (ranked 72) v Donna Vekic (ranked 84) so Heather's highest ranked opponent this week.
Next is Johanna Konta v Ana Konjuh (ranked 37).
Lastly Jocelyn Rae & Laura Robson v Darija Jurak & Ana Konjuh (though that may get changed considering that she'll have played the previous match). Darija Jurak is easily the highest ranked doubles player.
Early days but Heather Watson has broken serve in the first set.
British number two Heather Watson beat Donna Vekic 6-2 6-4 to give Great Britain the lead against Croatia in their Fed Cup promotion play-off tie.
The 24-year-old recorded the win over the world number 84 in 80 minutes.
"As the week has gone on my opponents have been tougher, but I've also been playing better," said Watson.
"There was a fist pump at the end because it was a lot more close and tense towards the end of the second set."
