Venus Williams has reached the US Open quarter-finals for the second time in three years with a 6-3, 3-6, 6-1 victory over Carla Suarez Navarro of Spain.

The 37-year-old American is the oldest woman left in the singles tournament. She owns seven grand slam titles, including two in New York in 2000 and 2001.

Maria Sharapova knocked out of US Open by 16th seed Anastasija Sevastova Read more

The No9 seed Williams is trying to get to her third major final of the season. She lost to her younger sister Serena at the Australian Open and to Garbine Muguruza at Wimbledon. Venus Williams could return to the top five for the first time since January 2011 if she reaches the semi-final – and finish as high as No2 if she wins the title and other results go in her favour.

Williams will meet Petra Kvitova next at Flushing Meadows, after she beat the No3 seed Muguruza. Williams was effusive in her praise for her opponent, who has come back from a knife attack at the end of last year. “What she’s gone through is unimaginable, unreasonable. The world we live in is just shocking. So for her, I think to be playing well is such a blessing,” said Williams. “To be able to come out here and do what she needs to do, to clear her head, it’s such a beautiful thing to see.”

There was more success for US women earlier in the day when Sloane Stephens reached the last eight at Flushing Meadows for the first time by upsetting No30 seed Julia Goerges 6-3, 3-6, 6-1.

Playing in only her second grand slam tournament since missing nearly a year with a foot injury, Stephens advanced to face Anastasija Sevastova, who beat Maria Sharapova.

Stephens has won 12 of her last 14 matches. Her best result in any grand slam is the semi-finals of the 2013 Australian Open.