Maxime Cressy, an American qualifier, delivers the biggest upset so far.

Maxime Cressy, an American qualifier, produced the biggest upset so far of this year’s U.S. Open. Playing with a throwback serve-and-volley style and big-point panache, Cressy rallied from two sets down in the first round to defeat No. 9-seeded Pablo Carreño Busta in a fifth-set tiebreaker.

Like most of Cressy’s matches, it was a contrast in styles. He rushed the net whenever possible and sometimes when it did not seem advisable against Carreño Busta, a quick and fit Spaniard who has twice reached the U.S. Open semifinals and has one of the best baseline games on the tour.

The 6-foot-6 Cressy hit 44 aces, and his swashbuckling victory required him to save four match points in the final-set tiebreaker before prevailing 5-7, 4-6, 6-1, 6-4, 7-6 (7). The match was played on Court 4, an outside court that had yield a stadium-like atmosphere by the end as fans craned their necks to watch from nearby locations and packed into the top row of the practice court bleachers and peered down as Cressy scrapped and volleyed for the biggest win of his career.

Born in Paris — his father is French and his mother is American — Cressy, 24, later became a collegiate standout at U.C.L.A. and chose to represent the United States. He speaks French and English fluently, and his game speaks to the older generation of tennis stars who grew up playing the serve-and-volley tennis. That style has gradually disappeared: a victim of slower courts and the racket string technology that makes precise, dipping passing shots easier to produce. But the courts appear to be fast at this year’s U.S. Open, and Cressy was able to put his volleying skills and big wingspan to effective use when it mattered most.

He won 46 of 70 serve-and-volley points and 64 of 97 points at the net overall, frequently punching or chipping returns and pushing forward. “It’s great to see that style working on tour,” said Martin Blackman, the general manager of player development at the United States Tennis Association. “Quicker courts help but you still have to be able to hit those great volleys under pressure.”

Cressy hit plenty down the stretch, saving the first three match points when trailing 3-6 in the tiebreaker. The first two came on his serve and on the second, he hit two world-class low backhand volleys to stay in the point. On the third, at 5-6, Carreño double faulted, hitting his second serve weakly into the middle of the net. Cressy saved a final match point at 6-7 with another crisp backhand volley winner before closing it out: raising both arms high and howling as the crowd chanted “Maxime.” He then windmilled his arms to the crowd to celebrate.

Cressy is one of three former U.C.L.A. players who’ve advanced to the second round of this U.S. Open. The others are Marcos Giron and Cressy’s former roommate, Mackenzie McDonald, who defeated No. 27 seed David Goffin 6-2, 7-5, 6-3 on Tuesday and will next face Kei Nishikori of Japan.

Cressy will play Nikoloz Basilashvili, a former top-20 player, who advanced on Tuesday after Sebastian Korda, another promising young American player, retired in the second set because of a gastrointestinal problem.

But Cressy made sure that it was also a day of pleasant surprises for American men’s tennis, and he is the first American man to defeat a top-10 player in singles at the U.S. Open since Jack Sock beat Marin Cilic in the third round in 2016.