NEW YORK — Coco Gauff’s first match since enlisting someone to help with her shaky serving got off to a rocky start at the U.S. Open on Tuesday night. She double-faulted in the very first game — and a total of 10 times. She got broken in that game, too — and a total of six times.

The only numbers that truly counted in the end, of course, were the ones on the Arthur Ashe Stadium scoreboard, and those showed that the No. 3-seeded Gauff held on for a 6-4, 6-7 (2), 7-5 victory over Ajla Tomljanovic to reach the second round at Flushing Meadows.

“It wasn’t the best,” Gauff said, “but I’m happy to get through.”

Nothing came easily. Gauff twice led by a break in the second set but couldn’t end things. She went up 5-3 in the third and served for the victory at 5-4, but double-faulted twice in a row and missed a pair of forehands to make it 5-all.

“Staying close also puts her under pressure to serve it out,” Tomljanovic said. “In the first round, even if you’re Coco, it’s never easy.”

That slip-up could have been too much to take for Gauff. Instead, she steadied herself, broke right back, then was able to serve it out on her second chance to do so, nearly three full hours after the contest began.

“I had so many chances. … I was just like, ‘Eventually, one of these is going to go my way,’” she said.

Gauff, who won the first of her two Grand Slam titles at the 2023 U.S. Open as a teenager, added Gavin MacMillan to her coaching team shortly before the start of this tournament. MacMillan is a biomechanics expert who helped current No. 1 Aryna Sabalenka retool her serve a few years ago, and he was in the first row of Gauff’s guest box, seated right in front of her mother.

After beating Tomljanovic, Gauff called her practices with MacMillan “really tough” and “mentally exhausting.”

“I was spending a lot of time on court, literally serving until, like, my shoulder was hurting,” Gauff said. “I feel like it’s (going) in the right direction, and I think for me, it’s trying not to go back to old habits in those tighter moments, and I think I did that today, especially in the third set.”

The problem for Gauff, in a nutshell, has been a propensity to accumulate double-faults. Her 320 entering the U.S. Open were the most on the women’s tour this season — and more than 100 more than anyone else. That included 23 in one match earlier this month, then 14 the next time out.

On Tuesday, as she dealt with the work-in-progress of a tweaked service motion, Gauff began with much slower offerings than she’s capable of striking. As the match progressed, and the tension rose, the 21-year-old from Florida reverted to her customary pace, going from averaging just 88 mph on first serves in the first set, to 97 mph in the second and 101 in the third, when Ashe’s retractable roof was closed. She cranked one in at 117 mph and even produced one second-serve ace.

What won this one against the 79th-ranked Tomljanovic, an Australian best known for defeating Serena Williams at the 2022 U.S. Open in the 23-time major champion’s final match of her career, was Gauff’s exemplary court coverage and terrific backhand. Appropriately, a down-the-line backhand converted match point, and Gauff waved her arms overhead to rile up the crowd.

Even as Tomljanovic swung away on her big forehand, it was Gauff who got the best of their lengthy exchanges from the baseline.

She also fared well when she pressed forward, winning 12 of the 15 points she ended at the net, including one with a leaping, over-the-shoulder, back-to-the-net volley winner in the third set

This was Gauff’s first match at a Slam since stumbling to a first-round exit at Wimbledon in July, a setback that followed her championship at the French Open in June.

As Gauff moves forward at Flushing Meadows, there is a chance she can overtake Sabalenka and No. 2 Iga Swiatek in the rankings and rise to No. 1 for the first time.