NEW YORK — Novak Djokovic‘s quest to complete the calendar-year Grand Slam took another step forward Monday night as he downed American Jenson Brooksby 1-6, 6-3, 6-2, 6-2 to reach the quarterfinals of the US Open.

The 20-year-old Brooksby, a wild card entry ranked 99th, took the opening set 6-1 in 29 minutes, breaking Djokovic’s serve twice.

But it was all Djokovic after that.

Trying to complete the first calendar-year Grand Slam by a man since 1969, the top-seeded Djokovic shook off the loss of an exhausting 24-point game in the second set that cut his lead to 3-2, breaking Brooksby in the following game and then winning the next as well to regain control.

He then had a fairly easy time in the third and fourth sets as Brooksby showed signs of wearing down.

Djokovic, seeking his men’s record 21st Grand Slam title, is now 11-0 against Americans at the US Open.

Brooksby was trying to become the youngest American man in a major quarterfinal since Andy Roddick at the 2003 Wimbledon.

It was in the fourth round last year at Flushing Meadows that Djokovic was defaulted for accidentally hitting a line judge in the throat with a tennis ball after dropping a game in his match against Pablo Carreno Busta.

Now, he moves on to play sixth-seeded Italian Matteo Berrettini, a 6-4, 3-6, 6-3, 6-2 winner against Oscar Otte in the quarters. Djokovic beat Berrettini to win Wimbledon and give him 20 Grand Slam titles, tied with Roger Federer and Rafael Nadal for most by a male.

Earlier Monday, Olympic champion Alexander Zverev beat Jannik Sinner 6-4, 6-4, 7-6 (7) for his 15th straight victory. The No. 4 seed from Germany started that run in Japan, carried it through a title in Cincinnati and then kept right on going at the US Open, where he was the runner-up to Dominic Thiem last year.

“I’m happy where I am, I’m happy with how things are, and I’m happy with how things were the last few months,” Zverev said. “I’m in the quarterfinals now, and from here on, the matches will definitely not get easier.”

Zverev said his gold medal is with him in New York. The 24-year-old, who has been accused by a former girlfriend of domestic abuse, joked in his on-court interview that he cuddles with the medal when he’s in bed because he doesn’t have a girlfriend.

He said keeping the medal with him is a way to remind himself of his success over the last month. He pointed to the confidence he’s gained from it as a reason he pulled out a couple of close games late in the second set, then came from behind to take the tiebreaker.

“I think that’s maybe the last few months for me, right there,” he said.

Zverev’s winning streak includes a victory over Djokovic in the semifinals at the Olympics. He hit 17 aces Monday and will play South African Lloyd Harris, who eliminated No. 22-seeded American Reilly Opelka 6-7 (6), 6-4, 6-1, 6-3.

Information from The Associated Press was used in this report.