Rafael Nadal kept pulling away in his US Open quarterfinal, then getting reeled back in by Diego Schwartzman.

In the first set, Nadal led 4-0 before Schwartzman got to 4-all. In the second, Nadal went up 5-1 before Schwartzman made it 5-all.

It took more than two hours to play just those two sets. Eventually, both were claimed by Nadal. And so, ultimately, was the match and a berth in a 33rd Grand Slam semifinal for Nadal, who prevented Schwartzman from reaching his first by winning 6-4, 7-5, 6-2 after 12:30 a.m. ET Thursday in Arthur Ashe Stadium.

"Like a lion in the ... jungle. He's big. He's a fighter. He knows how to play the important moments, every single time," Schwartzman said. "I've played him eight times and every important moment, he played better than me."

No wonder Nadal is 8-0 against the guy.

Roger Federer and Novak Djokovic are both out of the bracket, but Nadal is still around, meaning at least one member of the Big Three is in the semis at a 62nd consecutive major tournament. That trio has combined to win the past 11 Slam trophies -- and Nadal is going to be heavily favored to make that 12.

None of the other men left has played in a major final, let alone won one. Nadal, though, is closing in on a fourth championship at the US Open and his 19th at all majors, which would move him within one of Federer's record for men.

On Friday, Nadal will play Matteo Berrettini. The 23-year-old from Rome gave Italy a spot in the final four at the US Open for the first time since 1977 in dramatic fashion, double-faulting away his initial match point and then needing four more to finally put away 13th-seeded Gael Monfils of France 3-6, 6-3, 6-2, 3-6, 7-6 (5) after nearly four hours.

The other men's semifinal Friday is No. 5 Daniil Medvedev against unseeded Grigor Dimitrov, who beat an injured Federer in five sets Tuesday night to become, at No. 78, the lowest-ranked semifinalist at the US Open since 1991.

A year ago, it was Nadal whose body broke down: He retired from his semifinal against runner-up Juan Martin del Potro because of a bad knee.

This time, on a muggy night with the humidity above 50%, the left-hander raised some concern by having a trainer come out to rub a cream into that forearm during a changeover early in the third set. At the next changeover, Nadal flexed his right forearm and was visited again by the trainer, took a salt pill and guzzled some drinks, then shook that arm between points in the following game.

Afterward, Nadal said he had dealt with cramps late in the second set and early in the third.

"And then I took some salt, that's all, and then it was over. The body is in good shape, I think. Not big problems," Nadal said. "Just, of course, a little tired. Long day."

Still, Nadal managed to play his best when it mattered the most against the 20th-seeded Schwartzman, an Argentine serenaded by loud choruses of "Ole! Ole! Ole! Ole!" by an audience that included former San Antonio Spurs star Manu Ginobili.

Nadal came up with a service break in the last game of each of the opening two sets, then the last one he would need made it 4-2 in the third and he broke yet again to end it.

"I don't know how," Schwartzman said, "but this guy is improving every time.''

Now Nadal becomes Berrettini's problem. The Italian's win Wednesday was hardly a thing of beauty, with both he and Monfils, clearly spent, fighting themselves and the tension of the moment as much as the guy on the other side of the net.

Monfils finished with 17 double faults but managed to avoid any throughout the entire exhausting fifth set until he served at 6-5 -- and then he had three in that game, plus another two in the deciding tiebreaker, often doubling over between points to rest and catch his breath.

"A very bad day for me, serving," Monfils said.

Berrettini acknowledged the obvious afterward, too, saying he felt "a little bit tight."

It all was a bit of a blur.

"Right now, I don't remember any points, just the [final] match point, you know?" he said. "I remember also the double fault; I have to be honest."

The match began on a muggy afternoon and concluded with the stadium's retractable roof shut after rain came during the third set.

Monfils, who is 10 years older, fell to 2-7 in major quarterfinals and could be forgiven for wondering how many more chances he'll get.

Berrettini, meanwhile, is on top of the world at the moment. With Corrado Barazzutti, Italy's only other male semifinalist at the US Open, back in 1977, in the stands Wednesday, Berrettini used his big forehand to produce 24 winners. He has found an Italian restaurant he loves on Manhattan's East Village and has been eating there throughout the tournament, and even had someone who works there in his guest box, wearing a shirt featuring the word "Carbonara."

The first match point came while Berrettini served for the win at 5-3 in the fifth. Two more came and went when Monfils served at 6-5. A fourth was erased by an ace by the Frenchman in the tiebreaker. But on the fifth, Berrettini's serve was returned long by Monfils.

Berrettini stared at the ball as it descended, making sure it landed out, so that he would in fact be moving on. He dropped to his back, spreading his limbs, then ripped off his hat as he rose to pound his chest.

He then proceeded to say "Grazie!" over and over during his postmatch interview, thanking "my family at home, my mental coach -- they care about me a lot."

And then, perhaps also as a reminder to himself, he told the fans who were pulling for him in the stadium: "The tournament is not finished yet, so be ready for the next match, guys."