Coco Gauff has officially taken over the U.S. Open, just like she did Wimbledon.

With her opening-match jitters behind her, Gauff survived a raging third set to continue adding to her young legacy Thursday night.

Gauff looked on the way to a rout, bludgeoning Hungary’s Timea Babos early to take a 6-2, 2-0 lead. But the 15-year-old got outmuscled in the second stanza before rising up once again to pull out a 6-2, 4-6, 6-4 second-round, 2½-hour thriller at raucous Louis Armstrong Stadium.

At her age, nothing is likely to come easy in her first Open, but she handled the mounting pressure with aplomb, outlasting the 26-year-old Babos for a second straight three-set win.

“She’s growing up right before our eyes,’’ her father/coach Corey Gauff told The Post. “Every time she gets on stage like this, it’s good experience. She finds a way to makes it happen for herself.”

And Coco-mania is growing, too. The phenom was more in rhythm early and steely late, admitting she was “less nervous.’’ Now the U.S. Open gets a glorious third-round battle Saturday between Gauff and defending champion Naomi Osaka.

In addressing the massive crowd support at Armstrong, Gauff told the throng in her on-court interview, “It’s so great that you guys really believe in me and you carried me through the first two matches. I hope you can help me Saturday and in my doubles [Friday].’’

“Let’s Go Coco,’’ the fans chanted deep into the rollicking third set as the stadium rocked with noise.

Gauff said she knew she’d be a crowd favorite, but it’s exceeded expectations.

“I was thinking like maybe they feel like I’m Golden State in Game 7,’’ Gauff said.

In the third set, Gauff blew a break point at 4-3, but then held serve at love to make it 5-4.

Gauff dug down deep across the third set, hit some terrific angles and a slew of unorthodox sliced shots and moon-balls that baffled Babos.

At 5-4 on Babos’ serve, Gauff got up match point after a baseline slugfest ended with Gauff coming to the net and hitting a spectacular backhand drop volley winner. Babos then pummeled a backhand into the net after a Gauff moon-ball ruined her rhythm.

“It was a great match — not just the third set,’’ Babos said.

Babos is more a doubles specialist, having won 21 titles, but she can be a gritty, smart singles competitor and it indeed became a sensational battle with a raft of long, gritty rallies.

The rangy, 5-foot-10 Gauff was flying all over the court, hitting the deck a few times while lunging for shots on the run. She got to all of Babos’ drop shots and the Hungarian abandoned that strategy.

“She’s super fast,’’ Babos said. “I had to win the point many times against her. She’s super talented with huge power. A 15-year-old with power on the serve, I wished I had that when I was younger.’’

Osaka, 21, is looking forward to their first meeting. Gauff talked about how nice Osaka had been to her since they met at the Miami Open when she was 13.

“She’s super sweet — I would love to play her,’’ Osaka said. “When I hear people talking about someone, I want to have the opportunity to play them just to assess it for myself. I definitely would love that.”

Said Gauff, “I’m just curious to see how my game matches up against hers.’’

Corey Gauff knows her daughter is not expected to win.

“She’s an underdog, but nobody’s undefeated,’’ he said. “There’s a way to beat everybody.”

A double-fault machine in her opening victory against Russian Anastasia Potapova, Gauff got her serve cranking early after she was broken in the first game. She broke right back and soared the rest of the set.

But then the double faults (seven total) returned to her game as she went for too much on her second serve.

During one of her breaks in the first set, Gauff dazzled by retrieving two balls going side to side on the baseline, then firing a backhand winner on her third great get. The place exploded as she went up 4-2, then she held at love for a 5-2 lead, pumping in an ace at 40-0. The fans ate it up.

“It’s great everyone’s cheering,’’ Gauff’s father said. “It’s sincere.”