Naomi Osaka, Petra Kvitova, Madison Keys into Brisbane International semifinals

Naomi Osaka battled for two hours while Petra Kvitova cruised to victory on Friday as both players booked spots in the season-opening Brisbane International semi-finals.

Osaka’s form slipped after the first set but the world number four eventually saw off sixth seed Kiki Bertens 6-3, 3-6, 6-3 at Pat Rafter Arena.

Bertens was on the attack in the second but lost control in the decider when she began to struggle with her first serve.