Stephens and Osaka are making their debuts at the season-ending event, and it was the American who opened Red Group action with a win built on the foundations of solid defence from the baseline and a devastating forehand when she attacked.
"I thought I played a really good match", Stephens said in her post-match press conference.
Osaka - who shocked Serena Williams to claim this year's grand slam in NY - fought back from a set down only to fade badly down the stretch, allowing Stephens to pick up the first points in the Red Group.
Kerber's victory evened up her record at 1-1 in round robin play as Osaka slumped to her second straight defeat, leaving the U.S. Open champion needing to beat Bertens in her final group match to have any hope of advancing.
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.
Kerber made the fast start in the Red Group meeting as she secured back-to-back breaks of serve before sealing the first set on her third opportunity.
Germany's Kerber had to draw on all her big match experience to hold off the challenge of the rising star of the women's game, 21-year-old Japanese player Naomi Osaka, and win 6-4, 5-7, 6-4 in Singapore on Wednesday.More news: Nageshwar Rao Is Corrupt: Prashant Bhushan..
There Osaka's momentum ended, as she swiftly found herself 1-4 down to a more inspired Stephens. "I think she played really well, and I think she deserved to win the match", she added.
After comeback, Bertens in the second game of a tennis player in the final set in seven games in a row couldn't protect his serve.
Osaka's serve deserted her in the final set as she was broken three times.
The second set did not disappoint with a competitive start before the break point chances came out to play.
The Dutchwoman only made it to Singapore when Romanian world number one Simona Halep withdrew through injury but she showed incredible grit and tenacity after falling a set and 2-0 down to fight back for her 11th win over a top-10 player this season. "This match was sort of a continuation of my last match in a way. that I didn't serve well". I don't really think you can do that against her, so definitely I think that's what made the difference. [Osaka] is a great player with a lot of confidence.
A pair of easy holds and an another break took her to 5-1, and the 2017 US Open victor sealed the contest on her second match point when an anguished Osaka double-faulted for the fourth time in the match.
Stephens, ranked sixth in the world, overcame an error-filled performance that included handing away a service break with five straight faults before clinching the first set.