The American, 25, won six of the last seven games to claim the match 7-6 (7-4) 2-6 6-3.

The victory means all four players in the Red Group can still qualify or be eliminated going into the final games.

Osaka has lost both her round-robin matches, but can progress if she wins and the other result goes her way.

In Friday's final round of fixtures, Osaka plays Bertens while Stephens faces Angelique Kerber, who beat Osaka earlier on Wednesday and has one win from two.

Stephens and Bertens, 26, traded breaks throughout in a match which saw momentum change regularly.

Fifth seed Stephens won the first-set tie-break, before Bertens broke three times in the second set to win it in 36 minutes.

The third set continued the trend as the Dutchwoman won the first two games before Stephens took the match away from her. The 25-year-old now has two wins from two in the group stage, while Bertens has one.

• WTA Finals: Everything you need to know

Earlier on Wednesday, Kerber beat Osaka 6-4 5-7 6-4 in a match that included 11 breaks of serve.

Germany's Kerber, 30, won the first set and was a break up at 5-4 in the second, but the Japanese fought back to level the match. Kerber then won the final set to clinch the match, which lasted 2 hours and 31 minutes.

There is a similar situation in the White Group, in which Elina Svitolina, Karolina Pliskova, Caroline Wozniacki and Petra Kvitova can all still qualify after two matches.

The WTA Finals feature the top eight players this year, split into two groups of four. The top two from each group progress to the semi-finals, with the final on Sunday.

The WTA explains all the permutations, as all eight players in both groups of four can still qualify for the semi-finals.