NEW YORK — For a moment Tuesday afternoon, Emma Navarro’s storybook run at the US Open appeared to be at risk.

The New York City-born Navarro won the first set of her quarterfinal match against Spain’s Paula Badosa, 6-2, at Arthur Ashe Stadium, but she fell behind, 5-1, in the second set.

But Navarro dialed in.

Navarro, 23, stormed back to win six consecutive games and improbably take that second set, 7-5, as she advanced to her first-ever semifinal at a Grand Slam event.

The furious comeback saw Navarro win her last 12 points on serve, break Badosa’s final three serves, and at one point claim 17-of-18 points.

Navarro clinched the victory with a perfectly placed match-point finesse shot that bounced twice before Badosa could reach it, then raised her hands in the air as a near-capacity crowd showered her with cheers.

“Things weren’t looking great there in the second set, but just tried to be really tough, stick in there, make her hit one more ball,” Navarro said. “I felt like if I could scrap out a few longer points, maybe put some pressure on her, I felt like I could come back and maybe close it out in two sets.”

Once the world’s No. 2 player, Badosa entered this year’s Open as the 26-seed.

On Tuesday, Badosa dialed up her serve to 119 mph — playing with significantly more power than Navarro, whose serve maxed out at 107 mph — but came up short down the stretch. She committed back-to-back double faults during the 10th game of the second set, helping Navarro tie the match.

“I felt like she wasn’t totally confident in her ability to close out that set,” Navarro said. “I felt like if I could push back a little bit and make her think a little bit on her service game, maybe I could sneak my way back in there.

“Sometimes, you’re out on the court and you can kind of picture yourself playing a third set,” she continued. “When I was out there, I didn’t picture myself playing a third set.”

Badosa, who was also born in New York City before moving as a child to Barcelona, described her performance as a “disaster.”

“When I walked onto the court, I think I didn’t manage well, the situation or the emotions,” Badosa said. “It’s a bit hard to handle for me. I wanted to win so much that sometimes that doesn’t help at all.”

That instant-classic second set added another chapter in a momentous tournament for Navarro, who upset fellow American and defending Open champion Coco Gauff in three sets in Sunday’s fourth-round match.

Navarro grew up in South Carolina, though her New York roots remain a source of attention during the two-week tournament in Queens. Her grandmother lives about 125 miles away in Mystic, Conn., and has attended Navarro’s Open matches with her aunt and uncle.

Navarro was eliminated in the first round of her first two trips to the Open, including last year. Now the world’s 13th-ranked player, Navarro also defeated Gauff at Wimbledon over the summer en route to the quarterfinal.

The daughter of billionaire businessman Ben Navarro, Emma could be joined in the semifinal by Buffalo-born Jessica Pegula, whose parents own the Bills and Sabres.

Pegula — who, at No. 6, is the top-ranked remaining American — is set to face top-seeded Iga Swiatek in a quarterfinal match Wednesday. She would not face Navarro until the Open final.

“I did have access to resources as a kid,” said Navarro, whose dad is the founder and CEO of Sherman Financial Group, “but I don’t want that to take away from the fact that I’ve worked really, really hard to be where I’m at.”

She’s now two wins away from her first Grand Slam title — in her home city, no less.

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