NEW YORK -- Their combined ranking is somewhere past No.1,000, but that wasn’t why the USTA scheduled them Friday afternoon in the world’s largest tennis stadium.

Rather, it was more of a nod to the circular journeys of Caroline Wozniacki and Jennifer Brady, two superb athletes who left the game for very different reasons. This is only the third event since January 2020 for the recently unretired Wozniacki and, after a series of paralyzing injuries, Brady’s fourth since the summer of 2021.

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It was marvelous to see them trading shots in Arthur Ashe Stadium, a familiar venue to both. From 2009-16, Wozniacki advanced to the semifinals here five times, while Brady reached the same stage in 2020, losing to eventual champion Naomi Osaka.

In their first-ever meeting, Wozniacki was fitter and fresher in the end. A 4-6, 6-3, 6-1 winner, she advanced to the fourth round, her best effort at a major in more than five years. Wozniacki won 10 of the last 11 games.

When her signature backhand-down-the-line wasn’t firing, down a set and 0-2, Wozniacki started going crosscourt -- and turned it around.

“I played really, really well the last set and a half,” Wozniacki said in her on-court interview. “It’s such an honor to be here.”

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On Sunday, she’ll play No.6 seed Coco Gauff. It will be the first meeting between the two stars.

“Honestly,” Wozniacki said earlier this week, “I didn’t play for a very long time. I didn’t even touch my racquets. I didn’t know where they were. I didn’t miss it. I played since I was obviously very, very young. It’s been part of my life and my lifestyle for so long. I needed a break.”

It was after Wozniacki, now 33, brought daughter Olivia and son James into the world that she decided she wasn’t quite ready for pickleball. Missing the cardio component of training, Wozniacki started hitting a few balls -- and soon, she found, she did miss the sport.

“I’m very excited to have this opportunity and to play again and play at the highest level,” she said. “When you look at yourself and you feel like you still have a chance to do something really cool and really good, then you got to take the chance. You never know if you don’t try it.”

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For Brady, a 28-year-old American, the absence wasn’t a choice. Foot and knee injuries took her out of play and seriously threatened her career.  

“The toughest part,” Brady explained, “is just not knowing when you’re going to compete again. The unknown is something that -- it’s scary. It’s tough, but I’m here, I’m feeling pretty good.”

On the day of her first-round match against Kimberly Birrell, Brady woke up shaking.

“But it was good,” she said, “because it means something to me. I know that I was going to go out there feeling nervous, knew I wasn't going to play my best tennis. I just had to compete, find a way, and just stay in it.”

In a larger sense, both of these women found a way to stay in the game they cherish.

Wozniacki scored the first break to take a 2-1 lead. But Brady broke back immediately and the match settled into a comfortable rhythm. Brady, taking huge cuts at the ball, Wozniacki and her trademark defense, running most of them down. But with the Dane serving at 4-5, Brady turned it up. After Wozniacki cracked her racket a few times along the baseline in frustration, Brady broke her again, at love.

The two traded early breaks in the second set before Wozniacki hit a backhand behind Brady, converting her fourth break opportunity of the game to take a 4-3 lead. There was a moment in the next game that was telling. At 30-all, Wozniacki hit a drop shot that seemed reachable -- but Brady didn’t make a move for it at all.

Wozniacki broke her again to take the set and seemed to have the advantage of superior fitness. In her second-round, three-set victory over Magda Linette, Brady said she could feel her legs going in the second set and started to hit the ball flatter, leading to shorter points. Against Wozniacki, she seemed content to back off a bit and that played into the Dane’s trademark defense.

With some vintage side-to-side retrieving, Wozniacki forced a break point -- and took a 2-0 lead in the final frame when Brady hit an overheated forehand into the net. Inevitably, she ran out the set.

In the end, Wozniacki was more efficient, converting six of 12 break points. She was credited with 21 winners and 25 unforced errors, while Brady’s numbers were 24 and 36. Brady had 13 unforced errors alone in the third set, compared to only one for Wozniacki.

Wozniacki is now 41-13 (.759) at the US Open, her best winning percentage at any major.