No.8 seed Daria Kasatkina picked up her first career win at the WTA Finals with a 7-6(6), 6-3 round-robin victory over No.4 seed Coco Gauff on Thursday night in the Tracy Austin Group.

"It was tough," Kasatkina said afterward. "I was nervous at the beginning. ... With the rhythm of the match, nerves disappear a little bit and start to be better. So I'm really happy to be in the next round, still alive."

Still in the hunt for the title, Kasatkina will face Caroline Garcia on Saturday, with the winner of that match advancing to the semifinals. They have a 1-1 head-to-head, with Garcia winning at 2019 Wuhan, and Kasatkina prevailing at 2021 San Jose.

"This is exactly what we face every single week," Kasatkina said. "If you win, you advance, if you lose, you go home. ... So it's gonna be fun. The last tournament of the season for me and facing this kind of situation."

More from Thursday: Swiatek downs Garcia

With the win by Kasatkina, Iga Swiatek clinched the top seed in the group, while Gauff was eliminated from semifinal contention.

Battling the best: In the 1-hour and 40-minute match between two players making their WTA Finals debuts this year, Kasatkina maintained her undefeated record against Gauff, improving to 3-0 over the American teenager (6-0 in sets).

Kasatkina is now 5-2 against Top 5 opponents in 2022. Her two losses to Top 5 players this year both came against Iga Swiatek, in the Roland Garros semifinals and two days ago in her opening round-robin match in Fort Worth.

Against Gauff, Kasatkina kept her game tidy, with 14 winners matching her 14 unforced errors. By contrast, Gauff had 26 winners, but those were overridden by 43 unforced errors.

The win adds to a career-best year on hard court for Kasatkina. It is her 25th victory on the surface this season, which is already her highest annual tally.

Match moments: A topsy-turvy opening set saw Kasatkina come back from 4-1 down to hold a set point at 6-5. Gauff staved off that chance after a lengthy rally, and the pair moved into a decisive tiebreak.

In the breaker, Gauff took a 3-0 lead, but Kasatkina stormed back again, earning two more set points thanks to increasingly heavy forehands.

Kasatkina FH placement

Hawk-Eye Innovations

On Kasatkina's third set point, a Gauff forehand miscue found the net, and Kasatkina took the one-set lead after 66 minutes.

Based on her history, it was a crucial opening frame for Kasatkina, as she is now up to 29-0 this season after she wins the first set. The second set also went back and forth, but Kasatkina broke in each of Gauff's first three service games.

Kasatkina held on from there to keep her title hopes active, despite her opening loss to Swiatek on Tuesday.

"Normally if you lost, you're just like, 'OK, the tournament is done,' I pack my bags and I go to the airport," Kasatkina said. "Here is completely different. I had to push myself to practice the next day like nothing happened and prepare for the next match.

"That was interesting. I felt unusual, let's say, but pretty happy how I handled the situation, which was quite new for me."