NEW YORK — Coco Gauff needed this.

When you’ve lost your last five matches against top-50 opponents, you win anyway. You definitely win at the US Open at Arthur Ashe Stadium to secure a spot in the fourth round of your own Grand Slam. On Friday afternoon, the world No. 3 claimed that victory, coming from a set down to beat Elina Svitolina 3-6, 6-3, 6-3.

Svitolina, the Ukrainian No. 27, is exactly the kind of opponent a player who has failed to record a top-50 win in five tries wants to avoid. In the years since the Russian invasion of her homeland and the birth of her daughter, Skai, steel and assurance have become the defining characteristics of her game. Gauff has struggled with those qualities of late, but this victory is a reminder of the determination that makes her the reigning champion in New York.

Gauff acknowledged her lack of form going into the tournament, but said she was unaware of her losing streak against the world’s best players. Records like this don’t go unnoticed in the locker room, and Gauff looked vulnerable to her rivals. Tatjana Maria, world number 99, went to Arthur Ashe thinking she could beat Gauff with a serve and a slice. She wanted to let the American set her own pace and lift the ball, and in turn make mistakes. It worked, for a set that Gauff endured with great willpower. By the second set, she had figured out that Maria wasn’t going to hurt her. She won 6-0. Afterwards, she said she had expected a slice about 70 times out of 100. Less than 99 times.

Coco Gauff’s forehand is a weak point in her game, but it earned her crucial points against Elina Svitolina. (Timothy A. Clary/AFP via Getty Images)

Against Svitolina, she delivered a performance that will feed both the skeptics and the believers. Gauff’s forehand, a known weakness on the WTA Tour, looked vulnerable for much of the match, as did her backhand in the first set. Her phenomenal defensive skills and fighting spirit may have offset some of that vulnerability, but the faithful will have paid more attention to how that forehand earned her the points that carried her to victory.

Gauff spent long stretches of the first set using her forehand to hit inside-out backhands. As a result, she hit a fairly routine groundstroke into the net when on break point at 3-3, and Svitolina promptly broke her serve in the next game. In an epic 37-stroke rally early in the deciding set, Gauff would have been better off hitting a forehand drive volley than a backhand. She won the point, but perhaps could have done so with a lot less stress.

The more reliable backhand also faltered, to the extent that she began practicing that stroke and her serve after the match was over. It was a pair of backhands that landed in the net that produced the decisive break in the first set.

In her on-court interview after the match, Gauff said she tried to be more aggressive from that point on. From the moment she fended off a few points at 2-2 that would have put her a set and a break down, she raised her game and pushed through to the finish line — fueled in part by memories of her comeback victories here last year.

Svitolina agreed.

“I feel like she went for it more,” she said at her post-match press conference.

That aggression allowed Gauff to shorten and dominate the points in the deciding set.

Gauff and Svitolina were almost neck-and-neck in rallies of 0-4 strokes in the first two sets (37-36 in favor of Gauff). In the third set, Gauff overpowered Svitolina, 22-11 on won rallies. She also started winning the longer rallies from the second set, after being down by a considerable distance in the first set. A lingering ankle injury did not help Svitolina, but she paid tribute to Gauff’s durability.

Elina Svitolina, ranked No. 27, was unable to capitalize on her first-set win. (Robert Deutsch / USA Today)

“It’s clear she gets a lot of balls back,” she said.

It wasn’t just about digging in. Gauff started to feel the ball late, and it was two consecutive winners on the otherwise loose forehand side that changed the momentum of the match. Her serve was also more of a weapon in the third set, failing only when serving for the match. She broke Svitolina to end it instead.

Next up for Gauff is Emma Navarro, who knocked her out at Wimbledon earlier this summer. In that match, Navarro’s use of slices and changes of pace befuddled Gauff, who angrily pointed at her box and coach Brad Gilbert, asking them to “give (me) something” that didn’t come.

“With Emma, ​​I felt like I literally had a mental breakdown on the court during that match at Wimbledon,” Gauff said Friday.

“Going into this match I expect her to play her best tennis. I have to be mentally all in from start to finish because she’s going to be a tough opponent.”

Gauff hasn’t been at her best against those tough opponents lately, at least when you look at the rankings. But she was good enough to beat one in Svitolina to continue her US Open defense. From now on, it will all be tough opponents, but Gauff feels prepared now.

“I’m glad I had this competition because I think it makes me competition-tough and prepares me for future challenges,” she said.

Gauff needed this.

(Top photo: Robert Prange/Getty Images)