The 10th-seeded Rybarikova had lost her opening match to Julia Goerges in the Azalea group.
"I had a tough match yesterday and I had to play against someone who was resting so it was not easy for me," Rybarikova said. "I was saying to myself that I had to win this match because I had so many match points and it would be really cruel to end the season like this."
Also, ninth-seeded Ashleigh Barty defeated Anastasia Pavlyuchenkova 6-4, 6-1 in the Rose group, while Anastasija Sevastova beat U.S. Open champion Sloane Stephens 7-5, 6-3 in the Camillea group.
The tournament in Zhuhai features the leading players on the women's tour who didn't qualify for the WTA Finals in Singapore last week. The 12-player tournament is divided into four groups of three, with the winner of each group advancing to the semifinals.