Paula Badosa went a step closer to defending her Indian Wells Open title as she ended Leylah Fernandez's run to reach the quarter-finals.
Badosa was calm under pressure against last year's US Open runner-up, saving five out of the six breakpoints she offered up in a 6-4 6-4 success.
Matters were less routine for third seed Iga Swiatek, who held her nerve to come back from a set down against three-time major champion Angelique Kerber.
Breakpoints were contested in six of the match's first eight games and Kerber made the big points count, but Swiatek went on to triumph 4-6 6-2 6-3.
Swiatek, 20, showed grit beyond her years as she broke Kerber's serve four times in the second set, cleaning up her first-serve percentage while the German was only able to win 31 per cent of her successful first-serves (4-13).
Both women hit over 70 per cent of their first-serves in the final set, with the difference coming down to the return game, where Swiatek won half of her return points (12-24), with Kerber struggling (5-22).
Swiatek will face American Madison Keys, who defeated Harriet Dart in a brisk 69 minutes, while Badosa goes up against Veronika Kudermetova, who overcame Naomi Osaka in contentious circumstances earlier in the tournament.
WTA Finals: Gauff ends Swiatek hoodoo to reach final four
Iga Swiatek's hopes of finishing as the year-end world number one were dashed after she fell to defeat against Coco Gauff at the WTA Finals on Tuesday.
Gauff earned her first triumph over Swiatek since the 2023 Cincinnati Open, emerging a 6-3 6-4 victor to reach the final four of the competition in Riyadh.
It means Aryna Sabalenka is now guaranteed to top the WTA rankings at the end of a calendar year for the first time in her career.
World number three Gauff finished the encounter with 10 winners to 33 unforced errors, 11 of which were double faults. Swiatek outpaced Gauff with 15 winners, but struck 47 unforced errors.
At the age of 20 years and 237 days old, Gauff is the youngest American to reach back-to-back semi-finals at the WTA Finals since Tracy Austin (1979 and 1980).
She is also the first player under the age of 21 to win both her first two round-robin matches at the year-end competition since Ana Ivanovic and Maria Sharapova in 2007.
"It feels great and despite our head-to-head I was still confident and I knew if I could find my game, I knew I had the chance to close out the match," Gauff told Sky Sports Tennis.
"I was just trying to be resilient and play it deep. The conditions are tough and the altitude is tough.
"I was trying not to give her too many unforced errors. It's just a game of cat and mouse in these conditions."
In Tuesday's other match, Barbora Krejcikova ended Jessica Pegula's hopes of qualifying for the semi-finals of the tournament with a straight-sets triumph.
The Wimbledon champion needed just 69 minutes to secure a 6-3 6-3 victory, serving 11 aces throughout the contest compared to Pegula's one.
World number 13 Krejcikova became the lowest-ranked player to win a match at the WTA Finals since Magdalena Maleeva (ranked 17th) defeated Daniela Hantuchova in 2002.
The Czech will also have confidence of claiming the crown in Riyadh having won her previous events in Tallinn, Ostrava, Dubai and Wimbledon when beating an opponent in the WTA's top 10.
"I was fighting for every ball and I felt that I really have to play my best tennis," said Krejcikova, who picked up just her 20th match win of the season.
"I was trying to be really solid and trying to put as many balls to the other side as I could.
"I’m definitely proud. I had some very high parts of the season, especially winning Wimbledon. That’s something indescribable.
"And being here in the Finals is a huge privilege. It’s nice to get the win and still be part of the event."
Djokovic withdraws from ATP Finals
Novak Djokovic has pulled out of the ATP Finals, which start in Turin later this week.
Djokovic pulled out of the Paris Masters last month, and the world number five will now not feature in the season-ending tournament.
The 37-year-old, who lost to Jannik Sinner in the Shanghai Masters in his last competitive appearance, is sat on 99 ATP Tour-level titles, and his wait for a 100th victory will now roll into 2025.
Djokovic confirmed on Tuesday that he would not be participating in the ATP Finals.
"I was really looking forward to being there, but due to ongoing injury I won't be playing next week," Djokovic said on social media.
"Apologies to those who were planning to see me. Wishing all the players a great tournament. See you soon!"
Jannik Sinner, Alexander Zverev, Carlos Alcaraz, Daniil Medvedev and Taylor Fritz have all qualified for the tournament.
Andrey Rublev, Casper Ruud and Alex de Minaur are the three players contesting for the remaining two spots.
WTA Finals: Sabalenka digs deep to reach semi-finals
Aryna Sabalenka became the first player to book her place in the WTA Finals semi-finals after her straight-sets win over Jasmine Paolini on Monday.
The Belarusian had to dig deep in the second set but prevailed in 91 minutes, beating the Italian 6-3 7-5 in Riyadh to secure top spot in the Purple Group after two games.
While Sabalenka cruised through the first set, she was almost forced to a decider, but saved two set points in the 10th game of the second to level the score at 5-5 before going on to claim the victory.
In doing so, she became the first player to reach back-to-back semi-finals at the tournament as world number one since Serena Williams in 2013-14.
Having won three of her previous four tournaments and won 22 of her 23 matches in that time, Sabalenka is now just one win away from securing the year-end world number one spot for the first time, a feat she can achieve if she beats Elena Rybakina on Wednesday in the final round-robin match.
And she can go into it with confidence after improving her record against top-five opponents in 2024, with this her fifth such triumph.
"I'm proud of myself. Not only myself, my team," Sabalenka said.
"We were able to overcome a lot of things. To be able to show such great tennis and become World No. 1. It's teamwork. It's not only me. The behind-the-scenes work nobody sees.
"But they do a lot for me. I really appreciate them for everything they do for me. This is motivation for me to keep winning on this court. Those guys deserve to be called the best team ever."
In Monday's other match, Zheng Qinwen kept her hopes of reaching the final four alive with her win over Rybakina.
The Olympic champion was forced to go the distance though, despite getting the first break in the first and second sets, but eventually came out on top 7-6 (7-4) 3-6 6-1 in just under two-and-a-half hours.
Since the event's inauguration in 1972, Zheng is just the second Chinese player to win a match at the WTA Finals after Li Na.
It was a milestone victory for the 22-year-old as well as she earned her 50th win of 2024, improving her record to 50-17, making her the first Chinese player in the Open Era to hit that mark in a calendar year, though she acknowledged she could have made things easier for herself.
"I was the one to make the first break, and then I let her back in the first," Zheng said.
"Then it happened again in the second. But in the third set, I talked to myself. I broke her first and I stayed focused.
"Finally, in the third set, I start to play my tennis again. So, I'm really happy to win the match."
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