Coco Gauff arrived in New York this month carrying significant unwanted baggage. Although her summer had not started badly at all, it had descended into disappointment with a slew of dispiriting losses in significant tournaments. In stark contrast to her circumstances last year, when she capped off the best run of her life with her first grand slam title, the American returned to the US Open still searching for her best.

In front of a rocking crowd in Arthur Ashe Stadium, Gauff took a positive step forward as she drew on her resilience and problem-solving abilities after a testing start, recovering from a set down to reach the fourth round with a strong 3-6, 6-3, 6-3 win over Elina Svitolina.

“It means a lot. I knew today was gonna be a tough match, every time, Elina she’s a fighter,” said Gauff. “I knew I had to bring my best tennis, I thought I played well. I served much better than last match except the last service game but overall I was proud of what I was able to do.”

While she had eased to this stage with two efficient performances, this match was always going to be the first real test of Gauff’s level and her readiness to mount a strong title defence. Svitolina has built a great career out of her defence, consistency and grit. Her base level is reliably high, meaning it usually takes a quality performance to defeat her.

Since returning to the tour after giving birth to her daughter, Skai, Svitolina, 30 in September, has tried to play more offensive tennis instead of relying on her consistency and the hope that her opponents will miss.

She stepped out here looking to take the initiative, dictating most exchanges by injecting pace into both groundstrokes, especially with her forehand, and constantly looking to break down the Gauff forehand.

Although Gauff served well early on, she gradually lost her way. The Ukrainian continued to take the ball early and put her under significant pressure and Gauff particularly struggled with her trusty backhand. Down a break point at 2-2 in the set, she was on the verge of crisis.

Even as the match seemed to be slipping from her grasp, the 20-year-old from Atlanta, Georgia remained composed and she confidently navigated the most important moments.

Gauff saved the break point by forcing herself inside the baseline, eliciting a backhand error from Svitolina with a forceful inside-out forehand, before closing out an excellent hold.

Surviving that difficult game provided the world No 3 with the impetus she had been searching for all afternoon. She produced a spectacular return game to break serve in the next game, firing four winners in total, including two forehands, to close it out, and then she never looked back. From 2-2, break point down in the second set, Gauff won nine of the next 11 games before closing out an important victory.

The manner that Gauff found a way through was particularly encouraging for her hopes of another deep run. Her defence, physicality and her ability to win when she is not playing well are all qualities that have allowed her to keep rising at a young age, but she knows that she also needs to take the initiative herself. In the decisive moments here, it was important that she served well and had the confidence and quality to step inside the baseline and attack off both groundstrokes.

Less than an hour after Gauff had celebrated her win with fist pumps and a jubilant roar, she was back on the practice courts working hard on fortifying her backhand, one eye already on the next challenge.

“I’m just trying to go out here and have fun,” Gauff told Sky Sports. “I know from winning one that just from the fourth round it’s still so far, a long way to go.

“I’m just focused on the match in front of me and just enjoying it. I wrote in my journal: ‘I don’t want to leave with any regrets.’ Regardless of the results, I was just trying to give myself the best opportunity to win.”

Gauff will next face her fast-rising compatriot Emma Navarro, the 13th seed, who defeated her in the last 16 of Wimbledon last month. Navarro reached the fourth round in New York with a similarly tough 6-4, 4-6, 6-3 win over Marta Kostyuk, the 19th seed. Elsewhere, Zheng Qinwen, the Olympic champion and seventh seed, continued her run by easing past Jule Niemeier 6-2, 6-1.