In men's singles event, Nadal battled past 2014 titlist Marin Cilic 6-3, 3-6, 6-1, 6-2 on Monday night to reach the last eight at the Flushing Meadows for the ninth time.
"It's easy to describe, but difficult to make. I don't know, I think I followed the ball good because he had a good volley and I saw it, I ran fast to the ball and I saw at the last moment there maybe be a small space on that side," the ATP Tour website quoted Nadal as saying on court after the match. "I think it was the only way to win that point. I hit it well, but to hit that spot you need some luck."
With the Spaniard advancing and defending champion Novak Djokovic retiring to Stan Wawrinka on Sunday, tennis fans can expect a much-anticipated Roger Federer-Rafael Nadal final at the US Open.
The two have somehow never met in Flushing Meadows. However, for that to happen, Nadal will first have to get past Diego Schwartzman, who took out No. 6 seed Alexander Zverev earlier in the day.
Meanwhile, in women's singles event, top seed Osaka was stunned by Belinda Bencic of Switzerland 7-5, 6-4 in the fourth round at the Arthur Ashe Stadium.
The result also means that Osaka who was bidding to become the first woman to defend the title in New York since Serena Williams reeled off three in a row, between 2012 and 2014 will lose the world No. 1 ranking after the tournament to Roland Garros champion Ashleigh Barty of Australia.
"The challenge cannot be bigger than Naomi," said Bencic after the match. "I had to be at the top of my game. I'm pleased with how I managed my nerves."
"I had to take her serve early, try to anticipate, because she has a lot of power," she added. "I tried to play it a little bit like chess and tried to anticipate on the court."
Bencic will now face Donna Vekic of Croatia who defeated Julia Goerges from Germany in another fourth round match for a place in the semis.
( With inputs from IANS )