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NEW YORK — Karolina Muchova already had shot of the tournament sewn up when she produced an early contender for the best performance of the U.S. Open so far.

Muchova’s 6-3, 7-6(5) win over Naomi Osaka last Thursday night was a masterclass of variety and shotmaking. In one service game in the second set, Muchova held to love thanks to two volley winners, an ace, and a devilish slice that a discomfited Osaka could only flub into the net.

Osaka wasn’t at her best, but rallied in the second set, and briefly threatened to overpower her opponent. As a packed Arthur Ashe stadium illustrated, she remains one of the biggest draws in tennis despite her status as a wildcard entrant. A similarly rammed Louis Armstrong Stadium watched her overpower No. 10 seed Jelena Ostapenko Tuesday, and at the French Open in late spring, her encounter with world No. 1 and eventual champion Iga Swiatek electrified a dreary first week.

There was disappointment, still. Osaka said her “heart dies” when she loses, and her team had trailered the American hard-court swing as the moment that her return to tennis would explode.

Saturday, Muchova stormed into the last 16, dismantling Anastasia Potapova 6-4, 6-2, in another display of textured tennis. And then on Monday, she took on the women’s story of the year, Italy’s Jasmine Paolini. Paolini had reached two consecutive Grand Slam finals, playing a confident, smiling brand of tennis that leaned into her stature rather than trying to play around it.

Muchova beat her 6-3, 6-3, flowing through the court again. After putting in one contender for the best performance of the tournament, now she has another. And despite their contrasting fortunes this year in New York, the return of Muchova and Osaka is a huge win for women’s tennis. Especially if they can stay fit.

Both players have been on the comeback trail this year. Muchova finally ended a nine-month absence after surgery on a serious wrist injury, and Osaka returned to the tour earlier this year after announcing her pregnancy 19 months ago. With the WTA Tour in an interesting place, as Swiatek dominates Roland Garros, Aryna Sabalenka does the same in Melbourne, and the other two Grand Slams stay more open, the top of women’s tennis welcomes back two more contenders.

Muchova is a quarterfinalist or better at all four Grand Slams, but her ridiculously high ceiling has been lowered because of terrible luck with injuries.

The current world No. 52, a 28-year-old from the Czech Republic, is a tennis player’s player. Seven-time Grand Slam champion Justine Henin told The Athletic in June that because of her variety and imagination, Muchova is one of her favourite players to watch. Osaka expressed similar sentiments after seeing it up close Thursday.

Karolina Muchova’s deft touch is a hallmark of her tennis (Robert Prange / Getty Images)

“She’s very athletic. She has a lot of variety,” Osaka said. “I enjoy watching her play and also playing her, even though sometimes it doesn’t go my way.”

Dissecting her own game, Muchova told The Athletic in an interview ahead of Wimbledon, “It’s who I am and how I like to play, what fills me up on the court. It’s just me. I wouldn’t like to play any other way — even though sometimes it’s too much. I enjoy it and I spoke with my team and we try to improve these things and I’ll try to keep on going this way.”

On Thursday, she said that she just enjoys playing this way. “It’s fun,” she said.

For those not so familiar with Muchova’s game, Thursday night offered a crash course. She rushed the net and volleyed far more often, and far more efficiently, than the vast majority of players on the tour are able to do. Muchova ended the match winning 13 out of 19 (68 per cent) points at the net, and she served and volleyed in clutch moments. She was accomplished from the baseline too, nicking the first break of the match in the seventh game with a feathered drop shot, and then wrapping up the set with two thunderous forehand return winners when Osaka next served.

Muchova and Osaka’s second-round match electrified the U.S. Open after a slumbering start (Luke Hales / Getty Images)

In the second set, Muchova hit some outrageous volley winners on the stretch, and dug in when Osaka served to take the match into a decider. Come the tiebreak, her relentless retrieval, and use of slice to disrupt Osaka’s rhythm, earned a horrible error on match point to bring proceedings to an end.

Now into the last 16, Muchova has come from a place that no tennis player wants to go. After that surgery in February, on the area of the body tennis players most dread becoming damaged, Muchova worried she might not play the sport again. Initially, she couldn’t get out of bed or brush her teeth, but gradually her strength returned and her mood improved. Going to regular concerts at home in the Czech Republic helped, where seeing English rock band Nothing But Thieves was a highlight.

She returned to the tour at Eastbourne, the British seaside grass-court tune-up, but withdrew after two matches to protect her wrist. She then lost to Paula Badosa in the first round of Wimbledon, in straight sets. Badosa, another player who has been cruelly affected by injuries, said her biggest advice to Muchova was to “have patience”.

“Maybe, to another player, I would say something different, but she’s so talented. Her level will come back.”

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So it’s proved. Less than two months on, Muchova has thrillingly knocked out a two-time champion out of the U.S. Open, and then a two-time Grand Slam finalist. She moves into the quarterfinals to face either Caroline Wozniacki or Beatriz Haddad Maia, neither of whom will be looking forward to seeing Muchova across the net.

As an unseeded player, the Czech will be a dangerous factor in tournament draws even before she improves her ranking (Luke Hales / Getty Images)

For Osaka, as she memorably puts it, the results haven’t been resulting during her comeback. Flashes of her top level, however, are a testament to what Badosa said to Muchova about patience, and the need for time and match reps to raise the floor to match the incredible ceiling. “She’s an amazing player, and I’m really happy to see her back,” Muchova said after her win.

The challenge now for both players is to put together a run of good performances, and to improve their rankings (from No. 52 for Muchova, and No. 88 for Osaka) so they’re not playing opponents the calibre of each other so early in tournaments. Osaka hasn’t been beyond the quarterfinal of an event since beginning her comeback on New Year’s Eve, while Muchova, only a few WTA matches into her return, has always been able to turn it on against elite players without that translating into titles. Per Opta, of the nine active WTA players to have beaten five former world No. 1s at Grand Slams, Muchova is the only one not to have won a major or Masters 1000 title.

Whether Muchova, or indeed Osaka, goes on to win big tournaments soon is not so much the issue. Their playing on the tour at all is a victory for tennis, because the sport benefits so much when they do.

(Top photo: Charly Triballeau / AFP via Getty Images)