– The events and the arguing and the booing that would make this U.S. Open final unique began when Serena Williams' coach made what she insisted was an innocent thumbs-up but the chair umpire interpreted as a helpful signal.

It was the second game of the second set Saturday, in a packed Arthur Ashe Stadium, and Williams' bid for a record-tying 24th Grand Slam title already was in real trouble because she was being outplayed by first-time major finalist Naomi Osaka.

Chair umpire Carlos Ramos warned Williams for getting coaching during a match, which isn't allowed. She briefly disputed that ruling, saying cheating "is the one thing I've never done, ever." A few games later, Williams received another warning, this time for smashing her racket, and that second violation cost her a point, drawing more arguing. Eventually, Williams called Ramos "a thief," drawing a third violation — and costing her a game.

"I have never cheated in my life!" Williams told Ramos. "You owe me an apology."

Soon, Osaka was finishing off a 6-2, 6-4 victory that made her the first player from Japan to win a Grand Slam singles title. That is not, however, what will be remembered about this match.

With jeers bouncing off the arena's closed roof, both players — the champion, Osaka, and the runner-up, Williams — wiped away tears during a trophy ceremony that was awkward for everyone involved.

Williams whispered something to Osaka and wrapped an arm around her shoulders.

"She just won. I'm not sure if they were happy tears or they were just sad tears, because of the moment. I felt like, 'Wow, this isn't how I felt when I won my first Grand Slam.' I was like, 'I definitely don't want her to feel like that.'" said Williams, who missed last year's U.S. Open because her daughter, Olympia, was born during the tournament.

Osaka is just 20, 16 years younger than Williams — and grew up idolizing the American, even asking her to pose for a selfie together at a tournament just a handful of years ago. Their age difference was the second-widest gap between women's finalists at a Slam in the professional era.

"I know that everyone was cheering for her," Osaka told the crowd, "and I'm sorry it had to end like this."

What was most problematic for Williams on the scoreboard was that she was unable to keep up with a version of herself. Osaka, who happens to be coached by Williams' former hitting partner, hit more aces, 6-3. Osaka hit the match's fastest serve, 119 mph. She had fewer errors, 21-14. She saved five of six break points. And she covered the court better than Williams did.

"She made a lot of shots," Williams said. "She was so focused."

Osaka never let Williams' back-and-forth with Ramos distract her, never wavered from playing terrific tennis. The one time Osaka did get broken, to trail 3-1 in the second set, she broke back immediately, prompting Williams to smash her racket.

That cost her a point, because of the earlier warning for coaching. Williams' coach, Patrick Mouratoglou, acknowledged afterward that he did try to signal Williams, but didn't think she had seen him — and added that he thinks every player gets coaching during matches.

"I never had any warning in my career for coaching. Strange to do that in a Grand Slam final," Mouratoglou said. "Second, we all know that all the coaches coach at every match, all year long, from the first of January all the way to the 31st of December. We all know it."