World number one Ashleigh Barty booked her place in the WTA Finals semi-finals, before Belinda Bencic profited as Naomi Osaka's injury replacement Kiki Bertens also retired.

Barty, a debutant at the season-ending tournament, like Bencic, defeated Petra Kvitova 6-4 6-2 to bounce back from defeat to Bertens in her second Red Group match.

The French Open champion made light work of sixth-ranked Kvitova in Thursday's first encounter.

Needing a victory to guarantee her progress, Barty claimed her first win over the Czech in five attempts in confident fashion.

After a break of serve midway through the opening set saw the Australian edge in front, she wrapped up the second in less than 40 minutes with a third match point.

While Kvitova had already been eliminated ahead of facing Barty, the other match was a straight shoot-out for a last-four place between Bencic and Bertens.

And it was the Swiss, having denied Bertens a place in the original field with her victory in Moscow this month, who advanced due to her opponent's retirement with illness.

Bencic started on the front foot but, after failing to take advantage of her first two break points, fell behind at 3-2.

Yet Bencic responded in impressive fashion to take four successive games and the set, before Bertens, who had taken a medical timeout, stated she could not continue, trailing 7-5 1-0.

Barty and Bencic will learn the identity of their semi-final opponents on Friday, with defending champion Elina Svitolina through in the Purple Group as Simona Halep plays Karolina Pliskova for the opportunity to join her.