Novak Djokovic said "I'll take your legs out, that's for sure" after digging deep to outlast American qualifier Jenson Brooksby in a physically demanding encounter at the US Open.

Djokovic – bidding to become only the third man to claim a calendar Grand Slam and first since Rod Laver in 1969 – rallied from a set down to prevail 1-6 6-3 6-2 6-2 en route to the quarter-finals in New York on Monday.

It was a brutal clash on Arthur Ashe Stadium, 20-time major champion and top seed Djokovic needed almost three hours to see off world number 99 Brooksby, who was making his debut at the iconic venue.

After being blitzed in a 29-minute opening set, Djokovic and Brooksby contested a gruelling 20-minute fifth game in the second set – the latter converting a sixth break-point chance.

Djokovic's physical superiority, however, was on display as the Serb star eventually powered past the spirited 20-year-old at Flushing Meadows.

During the last-16 matchup, former world number one Andy Roddick tweeted, in reference to Djokovic, "first he takes your legs… then he takes your soul".

Djokovic – who will face sixth seed Matteo Berrettini in a repeat of the Wimbledon final – said on court: "Thanks Andy, I take that as a compliment – only the first part.

"The second part, I don't take anybody's soul. Everyone has their soul, we're all beautiful souls so I appreciate everyone. But I'll take your legs out, that's for sure."

Djokovic hit 44 winners in the four-set triumph, to go with 41 unforced errors in a tricky clash under the Arthur Ashe lights.

With his hard-fought victory, Djokovic improved to 11-0 against Americans at the US Open. He is 29-3 at major events and 70-10 in ATP Tour-level matches.

The 34-year-old is on a 21-match winning streak against players from the United States since Sam Querrey snapped his 30-match slam streak at Wimbledon in 2016.

"Great quality match," Djokovic, who can break the record for most men's slam titles – currently level with injured pair Rafael Nadal and Roger Federer, told reporters. "He started off better. I've never played him. I didn't see him play too many times. Maybe few matches in the last few months. Haven't followed his career prior to that, so I didn't know much about him. Had to do some homework and some analysis.

"It's different stepping out on the court first time against someone that really has nothing to lose. He's a young, talented player that is very crafty. He's got the really all-around game. He was pumped. He had the crowd behind him, of course. He played a perfect first set. Everything he intended to do he executed it perfectly.

"On my end, I was just trying to find a rhythm, trying to read his game, trying to understand where I can find holes in his game and start to attack and shift the momentum to my side.

"That happened already at the beginning of the second set. I broke him early. He broke back. But I re-broke his serve right away. We had some very, very long rallies, long games. It took a toll physically I think on both of us at that point. But I managed to find the right serves. I served efficiently when I needed to, opening up the court.

"The third and fourth set were really, really good from my side. I felt I was more dominant. I decreased the unforced errors that were really high in the first part of the match. I just was kind of swinging through the ball better. Was a good finish. It wasn't a good start. But all in all, expected the battle, and I got that one. I'm pleased to overcome it."