Lucie Safarova prevailed in a marathon quarter-final encounter with Daria Gavrilova at the Aegon Classic on Friday, as Petra Kvitova ousted Kristina Mladenovic.

Safarova came from a set down to beat the ninth seed 6-7 (4-7) 6-3 7-6 (7-5) after three hours and five minutes on grass in Birmingham, where the Russian-born Australian wasted three match points in the decider.

"I don't know what to say, it was such an amazing fight between the both of us and I'm so happy I won," Safarova said.

A leg injury picked up during the tough battle could yet hamper her chances of reaching the final of the WTA Premier event at Edgbaston Priory Club.

"I strained it a little bit, but I will get a good treatment," the world number 41 said. 

"I pulled out of doubles, and I will get a good treatment and I hope I will be ready for tomorrow."

Safarova will take on fellow Czech Petra Kvitova next after the two-time Wimbledon champion overcame Kristina Mladenovic of France 6-4 7-6 (7-5).

Garbine Muguruza's passage into the last four was eased by the retirement of Coco Vandeweghe. The American had won the first set 6-4 and lost the second by the same margin before pulling out at the start of the third. 

And Muguruza's semi-final opponent Ashleigh Barty will also be well-rested, Italy's Camila Giorgi withdrawing from their match at 5-2 down in the first set.