US Open champion Osaka took to the court with tape on the back of her leg for a problem that flared up in her defeat to Angelique Kerber on Wednesday and was competitive for half a set before opting to withdraw after Bertens took the opener 6-3.
Kiki Bertens continued her dream debut at the WTA Finals when the versatile Dutchwoman reached the last four after Naomi Osaka retired from their final round robin match with a left hamstring injury at the end of the first set on Friday.
US Open champion Osaka took to the court with tape on the back of her leg for a problem that flared up in her defeat to Angelique Kerber on Wednesday and was competitive for half a set before opting to withdraw after Bertens took the opener 6-3.
"It's never nice to win a match like this and I hope she's feeling better soon," the 26-year-old Bertens said in a post-match interview. "I will just try to keep on going. I have had some tough matches here already this week but the day in between helps for recovery."
The Dutchwoman, only in the tournament after top seed Simona Halep withdrew through injury last week, will be joined in the semi-finals by either Germany's Kerber or American Sloane Stephens, who complete Red Group play later on Friday.
Perhaps mindful of the injury, Osaka went for her shots from the outset, a tactic that comes with the risk of giving away free points, while Bertens was content to keep the ball in play and pin the powerful Japanese player to the back of the court.
Both strategies worked in the early stages until Osaka pushed the limits a little too far in the seventh game and was broken after she sent a string of forehands either long or wide.
Osaka left the arena for a medical timeout after Bertens held easily to move 5-3 ahead, the 21-year-old returning with her thigh now heavily strapped and was immediately broken to love as she hobbled painfully around the baseline.
The popular Japanese player called for the trainer once more but tearfully succumbed to her fate after consulting with her coach to end her breakthrough season with a disappointing three straight defeats at the year-end championships.
Bertens, meanwhile, continues to thrive after showing marked improvement on all courts as opposed to her favourite clay surface, backing up her opening win over Kerber and three-set loss to Stephens with another solid display in Singapore.
The late match has become a shootout for the final semi-final berth with Kerber (1-1) needing to win to finish second behind Bertens, while a Stephens (2-0) victory would mean the American tops the group ahead of the Dutchwoman.
Elina Svitolina advanced to the semi-finals as White Group winner on Thursday, the Ukrainian joined by big-hitting Czech Karolina Pliskova in the last four.
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 "Kiki Bertens in action on Friday")
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