Cocomania is taking further hold of the US Open as it steers into Labor Day weekend – and there is no telling how bright the fireworks will get. American sensation Coco Gauff made it through a stiff test from Hungary’s Tímea Babos to win 6-2, 4-6, 6-4 on Thursday night before a rollicking crowd at Louis Armstrong Stadium that hung on every point.

In doing so, she became the youngest player to make it past the second round at Flushing Meadows since Anna Kournikova in 1996 – and set the stage for her biggest challenge yet. The 15-year-old ingenue from Florida moved through into a Saturday showdown against world No 1 and defending US Open champion Naomi Osaka, a third-round blockbuster that will almost positively be staged under the lights at Arthur Ashe Stadium.

“This is just the beginning, I promise,” Gauff said afterwards to the still-buzzing audience. And following a second straight exhibition of heat-seeking serves, exquisite shotmaking and veteran mettle belying her inexperience, who would doubt her?

Gauff, a former junior No 1 whose grown-up ranking has soared 544 spots to 140th in the span of seven dizzying months, sprang from the gate far better than in Tuesday’s first-round win over Anastasia Potapova, breaking Babos three times in the opening set and pinning her back with a booming first serve that clocked as high as 118mph, a faster top speed than all but four women at this year’s tournament.

But Babos, a qualifier ranked 112th in the world best known for her doubles prowess, settled into the match nicely in the second, patiently extending the rallies with flat groundstrokes from the baseline and relentlessly hammering Gauff’s forehand, which incredibly appears to be the only weakness in the teenager’s package. The Hungarian finally broke in the eighth game and consolidated immediately, winning 18 of the final 22 points of the second set to wrest the momentum heading into the decider.

A hush fell over the packed stadium when Gauff fell behind 15-40 on her serve in the opening game of the third, only for the American to rattle off four straight points to escape with the hold. The quality only climbed from there as the players wowed the crowd with swashbuckling rallies that at times used every inch of the court.

Babos continued to pound away at Gauff’s forehand side, but the American leaned into the challenge and began winning the longer exchanges she had buckled under in the second, drawing out points with shrewd defensive shotmaking and foot speed which already rates among the best on the tour. One nail-biting hold followed another deeper into the third as the crowd urged the American onward with chants of “Here we go, Coco, here we go!” and “Let’s go Coco!” that rang down from the upper deck of the 14,053-seat show court during changeovers.

Then Babos, serving to stay in the tournament at 5-6, finally blinked with a series of misfires from the baseline to go match point down. When the Hungarian dumped a backhand into the net after two hours and 22 minutes, Gauff raised both arms skyward in triumph as Armstrong erupted in applause.

“For me it’s still wild,” Gauff said. “The first round was the first time I actually had a chant, but today it was a lot louder and a little more consistent. I was thinking like maybe they feel like I’m [NBA team] Golden State in Game 7 or something. It’s different because you’re an individual player, so it’s weird. Most of the time you hear the chants, it’s for a whole team, not just for, like, me.”

No one who has been around tennis for very long wants to go too far too fast when it comes to Gauff, who entered Flushing Meadows on a current of breathless hype after her charmed Wimbledon run and has now earned more than $377,000 in prize money in her two grand slam main-draw appearances. The sport has seen too many child prodigies done in by the pressures of premature fame, even if those cautionary tales are less common today than in previous generations.

But it’s clear there’s something happening out here in Queens – and whatever it may be will only get bigger on Saturday when the remarkably poised teenager steps into the world’s biggest tennis stadium against the top-seeded Osaka, who has been compromised by a knee injury that forced her to retire from a quarter-final match in Cincinnati less than two weeks ago.

The two share a warm relationship: they have practiced together in the past and their families know each other. But one look at Gauff’s steely game face and extraordinary composure makes it clear that will have to be put aside on Saturday.

“She’s an amazing player,” Gauff said. “She’s defending champion. She’s won two slams. She’s No 1. She’s only 21. We’re both pretty young. But I’m a little bit newer to the game. So I’m just curious to see how my game matches up against her. Obviously I want to win.”