Nadal was in tight battle with No.22 seed Marin Cilic at one-set a piece when the Spaniard somehow returned two smashes and hit a trademark counter backhand across court to set up three break points.
After splitting the first two games in the third set, Nadal kicked it into gear.
In the first set, Nadal led 4-0 before Schwartzman got to 4-all. But I am still really surprised with the way this last four weeks have been going.
And Monfils, bidding to reach his maiden semi-final at Flushing Meadows, tasted defeat largely down to his serving problems. "I mean, I'm the only one left, so now he's cheering for me".
"Physically I am fine".
"This is a big day for American tennis", he said of the ATP and WTA Tour events that will begin stateside next month. "Today I made a step forward, in my opinion".
Nadal fired a forehand victor on match point to seal the victory and make his 40th quarter-final at a Grand Slam event. Nadal's experience, also, will come to his aid, and with the likelihood of a tiring Daniil Medvedev awaiting him in the final, will see this as his last great opportunity to win a fourth US Open title.
Meanwhile, Serena Williams kept her dream of a record-equaling 24th Grand Slam title alive as he demolished China's Wang Qiang in just 44 minutes.
"He is like a lion in the middle, you know, in the jungle".
Their paths have crossed before with Nadal attending Woods's Hero World Challenge in the Bahamas two years ago. "He knows how to play the important moments, every single time", Schwartzman said.
"Watching him on the golf course, has been an example, a real inspiration for me".
Nadal, who has won three of his 18 major championships at the U.S. Open, will be playing in his 40th Grand Slam quarterfinal.
However, Berrettini built a 5-2 lead thanks in no small part to more double faults from Monfils, and the deficit proved too much to overcome as he went long on a return and the 23-year-old sank to the ground in celebration. "But during that match, I was born and died 15 or 16 times, '" Berrettini said about his conversation with the mental coach he's worked with for several years.
"He's the greatest fighter ever in this sport", Berrettini said.
On the women's side, Swiss Belinda Bencic reached her maiden semifinals at the majors with a 7-6 (5), 6-3 win against Donna Vekic of Croatia. Tomorrow afternoon I'm going to start to think about what's the plan for after tomorrow, ' he said. During the win, Nadal impressed with his receiving as he won 47% of his receiving points which allowed him to break his opponent's serve on 8 occasions.
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