NEW YORK >> For half an hour and a full set at the start, then one particularly compelling and competitive game later, Novak Djokovic’s opponent in the U.S. Open’s fourth round, Jenson Brooksby, gave him fits and created a raucous atmosphere under the lights at Arthur Ashe Stadium.

That let Djokovic, above all, and everyone else, too, 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, No. 1 Djokovic improved to 25-0 in majors this year by winning 1-6, 6-3, 6-2, 6-2 tonight. He extended his pursuit of a true Slam and a record-breaking 21st major championship while also eliminating the last American singles player in the tournament.

It is the first time in the history of an event that dates to the 1880s that no man or woman from the host country reached the quarterfinals.

One key to the turnaround by Djokovic, as good a returner as there is: He broke in Brooksby’s initial service game in each of the last three sets.

Perhaps affected by the physical nature of the extended exchanges, 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.

His 6-foot-4 strides and reach, his anticipation, his variety including 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.

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.

But Djokovic quickly heard his own cheers. 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 points, 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.

Djokovic, a 34-year-old from Serbia, next meets No. 6 Matteo Berrettini of Italy in a rematch of the Wimbledon final,

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.

And 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 Emma Raducanu of Britain, and No. 4 Karolina Pliskova of the Czech Republic against 2019 champion Bianca Andreescu of Canada or No. 17 Maria Sakkari of Greece

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 bracket began with a tournament-leading 21 U.S. men in the field — the 14 Americans in the top 100 of the ATP rankings are more than any other country — and 13 entrants reached the second round, the most since there were 15 in 1994.

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

There were 22 American women in the field, also the most of any nation. But four withdrew before play began because of injury or illness: 23-time Grand Slam champion Serena Williams, seven-time Grand Slam champion Venus Williams, 2020 Australian Open champ and French Open runner-up Sofia Kenin and 2021 Australian Open runner-up and 2020 U.S. Open semifinalist Jennifer Brady.