Venus Williams says the extreme heat in Cincinnati this week has not affected her too much on her run to the quarter-finals. After beating Kiki Bertens in the second round, Williams reached the last eight with victory over Donna Vekic in three sets.

She won 2-6 6-3 6-3 and will play Madison Keys in the quarter-finals where she is 2.50 to win with Keys 1.50. The 39-year-old lost the first set against Vekic but rallied in the second, making fewer unforced errors and raced into a 5-1 lead.

Her Croat opponent came back with the next two games but Williams closed the set out and then, two breaks of serve at the start of the decider gave her the advantage. “I’m pretty pumped,” she said.

“When you’re winning, it’s fun. When you’re losing, it sucks. I’m happy to be winning, trying to prevent losses.” Serena was in the crowd watching her sister and having her support was a boost for Venus.

She added: “Super fun, I mean, she’s obviously taking time away from her baby girl to come see me. “It’s great to have that support. Obviously the support of my other sister here, too, Isha. I am never alone, that’s for sure.”

Meanwhile, top seed Ashleigh Barty, the French Open champion, is another player through to the last eight in Cincinnati. She beat Anett Kontaveit, coming from a set down to win in three and she faces the Greek player Maria Sakkari in the last eight.

In the men’s draw David Goffin plays Yoshihito Nishioka in the quarter-finals while top seed Novak Djokovic is up against Lucas Pouille. Venus Williams is 13.00 to win the Cincinnati title with Ashleigh Barty 3.60.