Naomi Osaka and Ashleigh Barty came through tough tests to win their opening Red Group games at the WTA finals in Shenzhen.
Japan's Osaka beat Petra Kvitova 7-6 (7-1) 4-6 6-4, in a match lasting two hours 39 minutes.
Australian world number one Ashleigh Barty recovered from losing the opening set to beat Belinda Bencic 5-7 6-1 6-2.
"It was a high-quality match - you have to capitalise where you can," Barty said.
"I want to end the year playing the best of the best."
Switzerland's Benic was hampered by an ankle injury and called for the trainer in the second set.
It appeared to affect the world number seven's game just as her opponent's confidence grew, and Barty dominated the third set as Bencic's challenge faded.
Earlier on Sunday, Osaka dominated a first-set tie-break after Kvitova missed three break points at 4-4.
But the Czech, who is ranked sixth in the world, fought back from a break down to take the second set and force a decider and made Osaka wait for her win, breaking her when she served for the match at 5-2.
"For me it was very difficult and usually there's first-round first jitters and you can't really afford it as she came hard at me from the beginning," Osaka said.
The WTA Finals event sees the world's top eight players compete in two round-robin groups of four, with the winners and runners-up advancing to the semi-finals.
Defending champion Elina Svitolina is in the Purple Group alongside world number two Karolina Pliskova, Simona Halep and Bianca Andreescu.
The doubles is also played in a round-robin format and in the Purple Group second seeds Hsieh Su-Wei and Barbora Strycova beat Sam Stosur and Zhang Shuai 10-5 in a Champions tie-break, having won the first set 6-4 and lost the second by the same score.
Fourth seeds Gabriela Dabrowski and Xu Yifan beat Barbora Krejcikova and Katerina Siniakova 6-4 6-2.