Sloane Stephens has reached the semi-finals of the WTA Finals after knocking out German top seed Angelique Kerber.

The American has won all three of her matches in Singapore and saw off world number two Kerber 6-3 6-3 to set up a last-four match with Karolina Pliskova.

Japan’s US Open champion Naomi Osaka retired from her match against Kiki Bertens with a thigh injury after the Dutchwoman took the first set 6-3.

Bertens will face Ukraine’s Elina Svitolina in Saturday’s other semi.

“I knew it was going to be a battle against one of the toughest players on the tour,” said Stephens, 25, who topped her group with the win and recorded her fifth straight victory over the reigning Wimbledon champion.

“So I just came out and played as hard as I could and am really pleased with the win.”

The four lowest-ranked players have progressed to the semi-finals in Singapore, with Kerber and Osaka eliminated along with Caroline Wozniacki and Petra Kvitova from the other group.

Osaka took a medical timeout at 5-3 down in the opening set and, after Bertens won the next game to take the set, the 21-year-old conceded the match.

“I saw her in the match before that she was struggling a little bit with the hamstring, and of course she was taped today, but I think in the beginning she was still OK,” said Bertens.

“It’s never easy or never nice to win a match like this, but it is what it is. I’ll take it and I’ll take my rest, and I have some more recovery time for tomorrow.”

Osaka was ranked as low as 72nd in the world in January, but has enjoyed a rapid rise, culminating in her US Open win in September.

The world number four’s maiden Grand Slam singles title at Flushing Meadows was overshadowed by Serena Williams’ outbursts at the umpire.

“It’s just been a lot of new experiences,” said Osaka. “I’m very grateful that I was able to have the opportunities that I had. I feel like I have matured. I hope I can say that.”

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