Stephens secures second straight win in Singapore
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.
The early match began tentatively with three consecutive breaks of serve falling in the German's favour as Osaka looked to dictate with her power, while Kerber was content to counter-punch off the back foot and keep the ball in play.
Osaka, who was often battling to keep her emotions in check, fashioned five break points when Kerber served for the set at 5-4 but the German was able to stave off all of them with some gutsy tennis and sealed the opener with a booming serve. Osaka's inability to make the most of her potent serve looked to have cost her the match when she was broken to love in the ninth game of the second set but she then reeled off three games in a row to level the contest.
The break was enough for Kerber to seal a brilliant win, with Osaka crushing a backhand into the net on the German's first match point.
"I had my chances in the second set but she played some unbelievable tennis to win that one, and it felt like there was only one or two points in the decider," Wimbledon champion Kerber said in a post-match interview.
"It was great to win such a great match and to be able to look forward to another one in two days from now."
Angelique Kerber produced a dogged display of defensive tennis to tame big-hitting Naomi Osaka 6-4 5-7 6-4 in a classic Red Group encounter between the winners of the last two Grand Slams at the WTA Finals on Wednesday.
In the late match, Sloane Stephens continued her dream debut at the eight-woman event when the American moved to the brink of the semi-finals after she rallied for a 7-6(4) 2-6 6-3 victory over fellow tournament rookie Kiki Bertens.