Naomi Osaka is all smiles during her two-set win over Coco Gauff on Monday at the U.S. Open in New York. (AP photo)

NEW YORK (AP) — Naomi Osaka smiled before her U.S. Open showdown against Coco Gauff began Monday — and after it ended. Between points, Osaka patted her left thigh and quietly told herself, almost in a whisper: “Come on. Come on.”

Once the ball was in play, Osaka’s strokes were loud and on-target, producing the sort of confident, consistent and power-swinging tennis that carried her to four Grand Slam titles and the No. 1 ranking.

In the biggest statement yet that she is back at the height of her game, and a real contender for the sport’s highest honors, Osaka eliminated Gauff 6-3, 6-2 in Arthur Ashe Stadium to reach her first major quarterfinal in more than 4 1/2 years.

“I was super locked-in, to be honest. I was really locked in,” said Osaka, a 27-year-old who was born in Japan and moved to the U.S. with her family at age 3. “I felt like everyone wanted to watch a really great match, and I hope that’s what you got.”

From her side, it certainly was.

The No. 23-seeded Osaka was better throughout than No. 3 Gauff, whose repeated mistakes during a tournament that’s been a near-constant struggle for her really made the difference. And Gauff’s body language was quite a contrast to Osaka’s. Gauff repeatedly would put her palms up or cover her face with a hand or gesture toward her team in the stands, looking confused or upset.

Osaka displayed the demeanor — and, importantly, the booming serve and other strokes — that carried her to hard-court Slam championships at the U.S. Open in 2018 and 2020, and at the Australian Open in 2019 and 2021.

It was at the French Open later in 2021 that Osaka helped spark a global conversation about mental health by revealing she felt anxiety and depression. She then took a series of breaks from the tour.

That most recent trophy at Melbourne Park was the last time Osaka had even made it as far as the fourth round at any major until this match against Gauff, a 21-year-old from Florida who owns two major trophies. The first came at Flushing Meadows in 2023 and the second at the French Open this June.

Osaka returned to the tour last season after a 17-month maternity leave. Her child, Shai, was born in July 2023.

“I’m a little sensitive, and I don’t want to cry, but, honestly, I just had so much fun out here,” said Osaka, who first played Gauff back at the 2019 U.S. Open, also in Ashe, and won that one, too.

“I was in the stands like two months after I gave birth to my daughter, watching Coco. I just really wanted an opportunity to come out here and play,” Osaka told the crowd. “This is my favorite court in the world, and it means so much for me to be back here.”

Gauff came out jittery at the start. Her problematic serve was fine; other strokes were the problem. She finished with 33 unforced errors — way more than Osaka’s 12.

Plus, Osaka’s serving and returning were terrific. She won 32 of the 38 points she served — 15 of 16 when first serves landed in — and never faced a single break point. She also converted all four break chances she earned.

Trying to rework her serve during this tournament with the help of biomechanics expert Gavin MacMillan, Gauff got broken right off the bat and was down 2-0 after just five minutes, dropping eight of the initial nine points while making five unforced errors.

Whether because it’s what the prematch strategy dictated or because of how the beginning unfolded, Gauff cranked up the velocity in her second service game. The results were unimpeachable. She hit four first serves in — each arriving no slower than 110 mph, with a high of 115 mph — and held at love with a pair of aces and a pair of service winners.

Still, this is where the key difference was: Osaka used her big forehand, her best stroke, to go after Gauff’s forehand, her worst stroke, and it worked wonders.

By the end of the first set, Gauff had made 16 unforced errors and Osaka only five. By the end of the match, 20 of Gauff’s unforced errors were off the forehand side.

SWIATEK REACHES QUARTERS AS WELL

Iga Swiatek also rolled into the quarterfinals, rallying from down 3-1 in the first set to beat Ekaterina Alexandrova 6-3, 6-1.

“At the beginning, I felt like she was playing really fast,” said Swiatek, who is seeking her second U.S. Open title and seventh in a Grand Slam. “I wanted to find my rhythm, but later on I really felt like I was in my bubble and in my zone.”

Rublev is out of the US Open

On the men’s side, 25th-seeded Canadian Felix Auger-Aliassime advanced by defeating Andrey Rublev 7-5, 6-3, 6-4 in a match in Arthur Ashe Stadium that took just over two hours.

Auger-Aliassime won for just the second time in nine career matches against Rublev, the No. 15 seed who slammed his racket after losing a point in the second set.

“As I won the first set, I felt like I was in control of the match,” said Auger-Aliassime, who at age 25 is in the quarterfinals of a Grand Slam tournament for the fourth time. “Good win considering our head-to-head, considering how good he is as a player.”

What else happened at the US Open on Monday?

Eighth-seeded Australian Alex de Minaur beat qualifier Leandro Riedi 6-3, 6-2, 6-1. He’s set to play Auger-Aliassime next. Top-ranked Jannik Sinner faces Alexander Bublik in the night session.

Who is on Tuesday’s schedule at the US Open?

Second-ranked Carlos Alcaraz faces Jiri Lehecka in one men’s quarterfinal. It’s American Taylor Fritz against four-time U.S. Open champion Novak Djokovic in the other, with the winners meeting in the semifinals Friday. In the women’s quarterfinals, Jessica Pegula plays Barbora Krejcikova, and top-seeded Aryna Sabalenka goes up against Marketa Vondrousova.

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