In the day's first match on Friday, world No. 1 Ashleigh Barty came back from one set down to defeat Petra Kvitova 4-6, 6-4, 6-3, reports Xinhua news agency.
Barty now faces Kiki Bertens, after the Dutch eighth seed defeated No. 3 seed Elina Svitolina 7-6 (6), 6-2.
Elsewhere in the women's draw, the tournament's last unseeded player was knocked out, after Russia's Daria Kasatkina lost 6-3, 7-6 (5) to No. 16 seed Caroline Wozniacki.
Though the Russian saved three match points in the second set tiebreak, Wozniacki had enough in the tank to see her off, and the Dane now moves on to a semifinal clash with number four seed Naomi Osaka, who rebounded from a set down to knock out 5th-seeded Bianca Andreescu 5-7, 6-3, 6-4 in the first meeting between the two young rising stars on the WTA tour.
In the men's draw, Andy Murray's injury-recovery journey ended with a 6-2, 7-6 (3) loss to the tournament's No. 1 seed Dominic Thiem.
Thiem will play Karen Khatchanov in the semifinal, after the Russian came from a set down to defeat Fabio Fognini of Italy 3-6, 6-3, 6-1.
No. 3 seed Stefanos Tsitsipas also defeated John Isner 7-6 (3), 6-3 and will play number two seed Alexander Zverev in the semifinals.