NEW YORK  -  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. Took more than two hours just for 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. Thursday in Arthur Ashe Stadium.

Meanwhile, Belinda Bencic reached her first-ever Grand Slam semi-final, fending off Donna Vekic to win 7-6(5) 6-3 in their last-eight clash on Arthur Ashe Stadium.

The pair appeared evenly matched through most of the first set, as Switzerland’s Bencic struggled for consistency on serve, firing off five aces but committing four double faults. The 13th seed took command of the match in the second set, committing just four unforced errors compared to 17 in the first. Croatian Vekic fired 28 winners during the match but failed to save critical break points against her, as an elated Bencic reached a new milestone in an injury-plagued career.

“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 last 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 only one of Federer’s record for men.

Today (Friday), Nadal will play No. 24 Matteo Berrettini, a 23-year-old from Rome who is Italy’s first male semifinalist in New York since 1977. Berrettini barely got there, edging No. 13 Gael Monfils 3-6, 6-3, 6-2, 3-6, 7-6 (5) on Wednesday. The other men’s semifinal will be No. 5 Daniil Medvedev of Russia vs. 78th-ranked Grigor Dimitrov of Bulgaria.

Dimitrov won a five-setter Tuesday night against Federer, who was hampered by an issue with his upper back. Medvedev won his quarterfinal in four sets against Stan Wawrinka, who had built a big lead in the fourth round against Djokovic when the defending champion stopped because of pain in his left shoulder. 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 “Olé! Olé! Olé! Olé!” 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.”