World number one Angelique Kerber overcame stern resistance from Slovakia's Dominika Cibulkova to win her opening match at the WTA Finals.
The German, 28, won 6-7 (5-7) 6-2 6-3 as the eight-player, season-ending event got under way in Singapore.
Romanian third seed Simona Halep beat American sixth seed Madison Keys 6-2 6-4 in the other match in the red group.
"Domi is a tough opponent - I knew that I had to play my best tennis," said top seed Kerber.
"I was trying to stay positive in the third set, play my game, be aggressive and just go for it. I was also really concentrating on getting my first serve in. It was a really close match."
Kerber replaced Serena Williams, who is absent with a shoulder injury, as the world number one last month, and arrived in Singapore as the player to beat.
"The pressure is different for me now," said the Australian and US Open champion. "It's a different situation and I have a lot more commitments to fulfil when I come here compared to before.
"But it's a challenge for me and I'm really trying to play my best tennis in the last tournament, in the last week of the season. Of course, now I'm a little bit relaxed after I won."
Halep had too much for Keys, making her tournament debut, and the Romanian said: "I think I played exactly what I had to play against her. I was focused. Everything went as I wanted, so I'm happy."
The round-robin stage will continue on Monday, when Poland's defending champion Agnieszka Radwanska plays Russia's Svetlana Kuznetsova, and Czech Karolina Pliskova takes on Spain's Garbine Muguruza.
Two players from each group will progress to Saturday's semi-finals.
|WTA Finals singles draw|
|1. Angelique Kerber (Germany)|
|3. Simona Halep (Romania)|
|6. Madison Keys (USA)|
|7. Dominika Cibulkova (Slovakia)|
|2. Agnieszka Radwanska (Poland)|
|4. Karolina Pliskova (Czech Republic)|
|5. Garbine Muguruza (Spain)|
|8. Svetlana Kuznetsova (Russia)|