NEW YORK — After more than three hours of pushing each other around the court, Iva Jovic outlasted Alexandra Eala 7-5, 3-6, 7-5 to book a spot in the US Open fourth round, the farthest she’s ever gone at her home Slam.

After splitting the first two sets, Eala broke in the first game of the third and consolidated to take the early 2-0 lead. Jovic broke back two games later, and from there it was a battle of superb shot-making, stellar defense, ferocious ball-striking and extended rallies, the momentum shifting back in forth in front of an enthusiastic Arthur Ashe Stadium crowd that was clearly pro-Eala for the majority of the match, but seemingly behind both players equally by the end of it.

After a Jovic double fault gave the break back in the decider, Eala held at love for a commanding 4-2 lead.

It would not hold. Jovic won the next game after two deuces, and then tied the match with a pinpoint winner off Eala’s serve. After a running forehand volley winner gave Jovic a 5-4 lead, she earned her first match point in the next game, a backhand that found the net. 

After Eala held, Jovic took the lead back, 6-5, with an ace at 40-15.

In the final game, on Jovic’s second match point, Eala hit a forehand into the net and the 18-year-old American fell to the ground in relief and exhaustion. When she got up, Eala was already on her side of the court for the congratulatory post-match hug.

Jovic was excellent at the net, winning 12 of her 15 points, and struck 44 winners to 27 unforced errors. Eala came in even more, winning 16 of 25 net points, and had 34 winners to 33 unforced errors.

Both returned exceptionally well, though Jovic was slightly more effective in the most critical moments, converting 9 of 17 break-point opportunities to Eala’s 8 for 20. 

“It took losing my earrings, falling literally flat out on the floor, cuts on my knees, mental breakdowns,” Jovic said of the effort required to pull out the victory. “It took literally everything.”

After the match, the World No. 14 looked at the stat sheet to confirm that what she had just experienced wasn’t a figment of her imagination.

“I couldn’t believe what just happened,” said Jovic, who before this week had never been past the second round in New York. “We were both in the positive with the winners versus unforced errors, so it was just really, really high level. That gives me a lot of confidence, to be able to beat someone who is playing arguably top five tennis right now, with the summer that she’s had.

“I think if I can replicate that, it’s going to be good.”

Jovic praised Eala not only for her remarkable performance on court, but also the grace, warmth and maturity she showed in defeat.

“It says a lot about her as a person,” Jovic said. “I’m going to start crying, but it says a lot about her as a person, to be able to do that after that type of match and still come over and hug me and wish me all the best. And even in the locker room, behind closed doors. That just says a lot about her and her character. She’s incredible.”

Jovic will play former US Open champion Coco Gauff next for a spot in the quarterfinals. Earlier in the day, Gauff beat Cristina Bucsa in straight sets to reach the Round of 16 in New York for the fifth consecutive year. 

Gauff and Jovic have played once on the WTA Tour Driven by Mercedes-Benz, a 5-7, 7-5, 6-2 win for Gauff earlier this year in Rome. The teenager is looking forward to getting another shot at the two-time Grand Slam champion.

“This is what you want,” she said. “Week 2 in the Slams, you’re playing one of the best players in the world. Obviously she’s playing quite well right now. But last time I played her, it was a little bit of a heartbreaker, and I had a lot of chances. Hopefully I can learn from that and replicate [tonight]. I think if I replicate this level, I’m definitely going to have my chances in that one.”