Petra Kvitova eliminated Spanish third seed and two-time Slam winner Garbine Muguruza 7-6 (7/3), 6-3 while Venus Williams beat 35th-ranked Spaniard Carla Suarez Navarro 6-3 3-6 6-1 in the US Open with the Czech stepping up her comeback post injury.

Tuesday’s quarter-final will match Czech 13th seed Petra Kvitova, a two-time Wimbledon champion, against US ninth seed Venus Williams, seeking her eighth Slam title and third US Open crown.

Williams is the oldest woman entered at 37 but was this year’s Wimbledon and Australian Open runner-up. She hasn’t reached three Slam finals in a year since 2002.

“I’m focused on myself and trying to be as aggressive as possible,” Williams said. “Nobody ever gives you a Slam.

You’ve got to take it and I’m going to try and take it.”

Kvitova, 4-1 all-time against Williams, missed five months after a knife-wielding home intruder injured her left hand last December.

“I worked hard to come back and be here. It means a lot,” Kvitova said. “I don’t have words to describe. It was a tough time. All five months were very tough.

“It was just a journey I didn’t know how it would end. If it ends here on the big stage it’s a happy end.”

Muguruza still leads the fight for World No.1 after the Open but will be overtaken if fourth seed Elina Svitolina makes the semi-finals or top seed Karolina Pliskova reaches the final.

Stephens missed 11 months with a foot injury and returned only at Wimbledon, but has won 12 of her past 14 matches for her deepest US Open run in six tries.

“I honestly couldn’t have asked for a better comeback,” Stephens said. “Making it to the quarter-finals here is unbelievable.”

In a men’s draw assured of producing a first-time Slam finalist, Spanish 12th seed Pablo Carreno Busta meets Argentine 29th seed Diego Schwartzman in the last-eight while South African 28th seed Kevin Anderson meets US 17th seed Sam Querrey, who beat German 23rd seed Mischa Zverev 6-2 6-2 6-1.

Anderson matched his best Slam run from the 2015 US Open by beating Italy’s Paolo Lorenzi 6-4 6-3 6-7 (4/7) 6-4.

“I got off to a great start the first two sets and imposed my game,” Anderson said. “I had to dig deep and it feels absolutely fantastic to get through.”

Carreno Busta, who has not dropped a set, ended Canadian 18-year-old qualifier Denis Shapovalov’s dream run 7-6 (7/2) 7-6 (7/4) 7-6 (7/3).

Shapovalov would have been the youngest Slam quarter- finalist since Michael Chang at the 1990 French Open and youngest at the US Open since Andre Agassi in 1988.

“The biggest lesson is that I’m able to compete with these guys,” Shapovalov said. “I still think I have a lot of work to do.”

Schwartzman eliminated French 16th seed Lucas Pouille 7-6 (7/3) 7-5 2-6 6-2. At 5ft 7ins (1.70m), he is the shortest Grand Slam quarter-finalist since Peruvian Jaime Yzaga at the 1994 US Open.