Defending champion Caroline Wozniacki earned her first victory at this year's WTA Finals, beating Petra Kvitova 7-5, 3-6, 6-2 on Tuesday.
Wozniacki, who became the first Danish woman to win a Grand Slam title at this year's Australian Open, is now 1-1 in her group. Kvitova is 0-2.
"I played much better today," Wozniacki said on court after the match. "I returned well. I served well. Against Petra, she's so powerful, you have to stay on your game. I just tried to stay focused and get a lot of balls back.
"I always believe in myself and when I'm out on the court I believe I'm going to win."
Wozniacki lost to Karolina Pliskova in her opening match, while Kvitova lost to Elina Svitolina. Pliskova and Svitolina will meet later Tuesday.
Kvitova, who won the WTA Finals title in her debut appearance at the year-end tournament in 2011, was the one taking chances on Tuesday. But Wozniacki played steadier defense and waited for the Czech to make mistakes.
Kvitova finished the match with 40 winners and 40 unforced errors. Wozniacki had 19 winners and 14 unforced errors.
Wozniacki, who broke her opponent in the first and fifth games of the deciding set, took a medical timeout to have her left knee bandaged when Kvitova was leading 3-1 in the second.
Meanwhile, Rising Japanese superstar Naomi Osaka has vowed to push through fatigue and atone for her error-strewn loss to Sloane Stephens in her WTA Finals debut in Singapore on Monday.
An error-prone Osaka struggled with her rhythm and faded badly against Stephens, who won 7-5, 4-6, 6-1 in two hours and 25 minutes.
The 21-year-old came into the season finale as the in-form player, having won 14 of her previous 16 matches and capturing the US Open.
It has been a whirlwind for Osaka since her stunning victory over Serena Williams at Flushing Meadows in September.
"I haven't gone home (to Florida) since the US Open. So of course I'd love to go home, but I'm here right now and I want to do well," she told reporters.
"I want to give them (fans) a good match to watch. So for me that's my main priority, and I'm not really tired of that yet. So I just want to keep seeing how far I can go."
Osaka, who had 46 unforced errors in first match, said she hoped to keep her emotions in check moving forward.
"I am a little bit apologetic for doing the stuff that I did," she said. "I feel like for me I play better when no one knows what I'm thinking. I think I learned a lot from today."