Naomi Osaka reached her first grand slam quarter-final with victory over fellow 20-year-old Aryna Sabalenka.

In one of the most highly-anticipated women’s matches of the tournament, between two players who are expected to face each other many more times on the big stage, it was Japanese-American Osaka who prevailed 6-3 2-6 6-4.

Sabalenka saved three match points in the final game and had a chance to hold for 5-5 only to double fault on Osaka’s fourth opportunity.

A very emotional Osaka said: “I was just thinking I’d never forgive myself if I didn’t win that one. I was thinking I have to fight for every point. Even if I break a leg I should try to fight for every ball.”

Sabalenka has been one of the form players of the summer and arrived in New York on the back of her first WTA Tour title in New Haven before beating Petra Kvitova in the third round.

Osaka, ranked one place higher at 19, has had a quieter time since lifting her first WTA Tour title in Indian Wells but has been in superb form at Flushing Meadows and carried a 22-game winning run into the match having won her last two contests in just 50 minutes each.

Although they are the same age, Osaka has been a factor at the top level for a couple of years while Sabalenka has only made her big breakthrough this season.

And that showed in the opening set as Osaka reined in her aggression, instead using angles to drag Sabalenka around the court and tempting her opponent to make mistakes.

But in the second set Sabalenka stopped missing, staying in the points longer and putting Osaka under immense pressure.

Sabalenka has played a huge amount of tennis this summer and often gone the distance – this was her 25th three-set match of the season compared to just four for Osaka – and it was she who made the first break for 2-1.

But Osaka hit straight back and it was her nerves that proved just the stronger in the end.

Last year’s runner-up Madison Keys is the highest seed left in the bottom half of the draw at 14 and she breezed through to the last eight again with a 6-1 6-3 victory over Dominika Cibulkova.

Keys has not really been talked about as a potential champion this year – and that suits her just fine.

“It’s kind of nice to be under the radar,” Keys said. “Either way, I’m pretty used to it. This one just seems like it’s a little bit more low key. There is a bunch of big stories, obviously. Serena is back. Sloane is playing really well. There is just a lot going on this year.”