Coco Gauff arrived in New York this month with a lot of unwanted baggage. Although her summer had started off well, it had turned into disappointment with a series of disheartening losses in major tournaments. In stark contrast to her circumstances last year, when she capped the best run of her life with her first Grand Slam title, the American returned to the US Open still looking for her best performance.

In front of a jubilant crowd at Arthur Ashe Stadium, Gauff took a positive step forward, calling on her resilience and problem-solving skills after a rocky start. She recovered from a set down to reach the fourth round with a strong 3-6, 6-3, 6-3 victory over Elina Svitolina.

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

Although she had come to this level with two efficient performances, this match was always going to be the first real test of Gauff’s level and her willingness to mount a strong title defense. Svitolina has built a great career on her defense, consistency, and perseverance. Her base level is reliably high, meaning that it usually takes a quality performance to beat her.

Since returning to the tour after the birth of her daughter Skai, Svitolina (30) has been trying to play more attacking tennis in September rather than relying on her consistency and hoping her opponents will miss.

She stepped forward here with the ambition to take the initiative, and dictated most of the exchanges by injecting tempo into both groundstrokes, especially with her forehand, constantly trying to break the Gauff forehand.

Although Gauff served well at the beginning, she gradually lost her way. The Ukrainian kept taking the ball early and put her under a lot of pressure. Gauff especially struggled with her trusted backhand. At 2-2 in the set, she was on a break point and was on the verge of a crisis.

Even when the match seemed to be slipping out of her hands, the 20-year-old from Atlanta, Georgia remained calm and controlled key moments with confidence.

Gauff saved the break point by forcing himself inside the baseline and drew a backhand error from Svitolina with a powerful inside-out forehand, after which she held on to the ball superbly.

Surviving that tough game gave the world No. 3 the momentum she had been searching for all afternoon. She produced a spectacular return game to break serve in the next game, hitting four winners in total, including two forehands, to seal it, and never looked back. From 2-2 down, down a break point in the second set, Gauff won nine of the next 11 games before sealing a major victory.

The way Gauff found her way was especially encouraging for her hopes of another deep run. Her defense, physical strength and ability to win when she’s not playing well are all qualities that have allowed her to continue to rise at a young age, but she knows she also has 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 from both groundstrokes.

Less than an hour after celebrating her victory with fist pumps and a cheering roar, Gauff was back on the practice courts working hard on her backhand, her eyes already set on the next challenge.

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

“I’m just focused on the race ahead of me and just enjoying it. I wrote in my diary, ‘I don’t want to leave with regrets.’ Regardless of the results, I just tried to give myself the best chance to win.”

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