The match was billed as a showcase of the next generation of transcendent talent in women’s tennis, and it lived up to that billing.

Naomi Osaka and Aryna Sabalenka — a pair of precocious 20-year-olds with top-20 rankings (Osaka is No. 19, Sabalenka is No. 20) and the kind of powerful games that have them tipped as future major champions — staged a gripping, back-and-forth battle Monday in the fourth round of the U.S. Open, won by Osaka, 6-3, 2-6, 6-4.

“I’ve always dreamed of playing here and going to the quarterfinals and further,” said Osaka, who was born in Japan and spent part of her youth on Long Island before settling with her family in Florida. “So I’m just glad I could do one of my goals.”

Later, she added, “The tournament’s still going on. I still have goals. I want to go further and further, and not just settle here.”

While Novak Djokovic had the stage of Arthur Ashe Stadium and the attention of the ESPN broadcast for his routine win, Osaka and Sabalenka had refurbished Louis Armstrong Stadium to prove why they’re ascendant.

Sabalenka, of Belarus, was the revelation of the summer hardcourt swing. She deployed her punishing groundstrokes (she finished with 28 winners to Osaka’s 22) to take two breaks of serve and convincingly win the second set — as Osaka had done in the first. In the third, after trading early breaks, Osaka claimed easy holds (a crackling early ace, at 119 miles per hour, was 2 mph off Serena Williams’ fastest serve of the tournament) and then squandered leads in Sabalenka’s service games. On the fourth match point, Sabalenka double-faulted. Osaka cried in her chair.

“I guess I was crying because I had to pull something from deep within myself, and I’d never really done that before,” Osaka said (in English, to a question asked in Japanese) of eclipsing her best finish at a major.

Theirs is the generation that has never known a world without an inspirational Serena Williams: When Williams made her U.S. Open debut in 1998, Osaka was 10 months old, Sabalenka 4 months old. Osaka’s reverence comes with knowledge of the draw.

“Well, for me it’s like no secret that Serena is my favorite,” Osaka said. “I hope I can play her here. That would kind of mean we have to meet in the finals.”

And why not? Unseeded Lesia Tsurenko awaits in the quarters, with Madison Keys possibly in the semis. The future might be now.