For 1 1/2 sets, including one particularly compelling and competitive 24-point game, Novak Djokovic’s fourth-round opponent at the U.S. Open — Jenson Brooksby, the last American left in singles — gave him fits amid a raucous atmosphere at Arthur Ashe Stadium.

That let Djokovic, above all, and everyone else, know that Brooksby — a 20-year-old wild-card entry from California who is ranked 99th and never before had been on this sort of stage — belonged. And then, not surprisingly, Djokovic showed why he is who he is and how he’s managed to move within three victories of the first calendar-year Grand Slam in men’s tennis in 52 years.

Settling in and sending messages, to the fans with roars and to Brooksby with some staredowns, the No. 1-ranked Djokovic improved to 25-0 in majors this year by winning 1-6, 6-3, 6-2, 6-2 on Monday night. He extended his pursuit of a true Grand Slam and a record-breaking 21st major championship, while also making this the first time in the history of the U.S. Open, an event that dates to the 1880s, with zero men or women from the host country in the quarterfinals.

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“Was a good finish. It wasn’t a good tart,” said Djokovic, who hopes to add a fourth U.S. Open title to a collection that’s been boosted by his ninth at the Australian Open in February, second at the French Open in June and sixth at Wimbledon in July.

He next meets No. 6 Matteo Berrettini of Italy in a rematch of the final at the All England Club.

One key to Monday’s turnaround: Djokovic broke in Brooksby’s initial service game in each of the last three sets.

“I wanted to wear him down,” Djokovic said, “and it worked.”

Affected by a left hip that bothered him earlier in the tournament, Brooksby was visited by a trainer after the second set and again after the third. Still, for someone who never had set foot on Ashe’s blue court until about two hours before the match, when he got a chance to practice there, Brooksby never seemed overwhelmed by the setting or the circumstances.

“We’re going to see a lot of him in the future,” said Djokovic, who would be the first man since Rod Laver in 1969 to win all four Slam trophies in one year. “I mean, he has the means. Now, obviously a lot of things have to come together. But he has a bit of an unorthodox game. Does a lot with the feel. He’s smart. He knows how to win points.”

Brooksby’s 6-foot-4 strides and reach, his anticipation, his variety that includes a well-disguised two-handed backhand slice, his think-steps-ahead point construction, his commitment to patterns drawn up by his coach at home in Sacramento since age 7, Joe Gilbert — all left Djokovic a tad discombobulated early.

“I knew it would be important to start strong, to impose my mindset and my strategy, my game out there,” Brooksby said. “I could see it working. I really did have a lot of confidence in myself out there that I can beat him, I can beat anybody.”

In the first set, Brooksby made one unforced error, Djokovic 11. And Brooksby won 14 of the points that lasted five strokes or more, Djokovic four.

When Djokovic netted an overhead to move Brooksby two points from the set, most of the spectators in the 23,000-plus-capacity arena — excited to be back after last year’s ban on audiences amid the pandemic — rose, clapping and screaming.

When Djokovic missed a return to cede that set to his foe, Brooksby waved both arms and heard more loud support.

“Electric. Awesome. I enjoyed it. I truly did,” said Djokovic, who soon would be hearing his own cheers. “You guys gave both of the players a lot of energy.”

He broke to go up 2-0 in the second set and punched the air and shouted. At 3-1 arrived an epic game: six break chances, nice deuces, 24 points in all, spread out over nearly 20 minutes. Djokovic pushed the ball into the net to end that game and make it 3-2, prompting Brooksby to hop and jump and windmill his arm and cry, “Let’s go!”

And then, quick as can be, Djokovic regrouped. With Brooksby gasping for air, Djokovic broke right back and, soon enough, the outcome was clear.

“The momentum,” declared Djokovic, a 34-year-old from Serbia, “was changed.”

The other quarterfinals on the men’s side: No. 4 Alexander Zverev of Germany vs. Lloyd Harris of South Africa, No. 12 Felix Auger-Aliassime of Canada vs. 18-year-old Carlos Alcaraz of Spain, and No. 2 Daniil Medevev of Russia vs. qualifier Botic van de Zandschulp of the Netherlands.

The women’s round-of-eight matchups: No. 2 Aryna Sabalenka of Belarus vs. No. 8 Barbora Krejcikova of the Czech Republic, No. 5 Elina Svitolina of Ukraine vs. 19-year-old Leylah Fernandez of Canada, No. 11 Belinda Bencic of Switzerland vs. 18-year-old qualifier Emma Raducanu of Britain, and No. 4 Karolina Pliskova of the Czech Republic against No. 17 Maria Sakkari of Greece.

Sakkari beat 2019 champion Bianca Andreescu 6-7 (2), 7-6 (6), 6-3 in a match that ended at 2:13 a.m., making it the latest-finishing women’s match in tournament history.

“I hope you will not be late for work tomorrow,” Sakkari told those fans who stayed until the end. “Go get some sleep and I’ll see you in two days.”

Brooksby’s exit — certainly no shame in losing to Djokovic, of course — followed the fourth-round departures earlier Monday by No. 22 seed Reilly Opelka from the men’s draw with a 6-7 (6), 6-4, 6-1, 6-3 loss to Harris, and by unseeded Shelby Rogers from the women’s draw with a 6-2, 6-1 loss to Raducanu.

Rogers upset Ash Barty, a two-time major champion who is ranked No. 1, in the third round, but was unable to produce the same level of tennis in what she termed a “pretty embarrassing” performance Monday.

The brackets began with 43 Americans in the singles fields.

“We’ve got a huge group of guys there,” Opelka said. “We just don’t have the world-beaters.”