NEW YORK — The U.S. Open threw the closest thing to a farewell celebration that Serena Williams would allow for her opening-round match Monday night, but if a party was all that the 23-time Grand Slam singles champion wanted, she could have thrown herself one and skipped all those hours of sweat on the hard courts back home in Florida.

Williams did not come to New York simply for a ceremonial send-off, to listen to another series of elegies about how she has changed this sport, how she has broken down barriers and paved the way for the next generation of Black tennis stars and female athletes.

There is another legacy that Williams possesses as much as all the others — as one of the world’s great competitors. And she came to New York to compete in a Grand Slam tournament, seemingly her final one, to once more put her best on the line against the finest players in the world on the sport’s biggest stage.

She got that and more Wednesday night as she won, 7-6 (4) 2-6, 6-2, outlasting Anett Kontaveit of Estonia, the world’s second-ranked player.

If that first appearance two nights earlier was about posterity and sweet send-offs, round two was about doing everything possible to win a tennis match in front of a whole new gallery of boldface names, like Tiger Woods, who sat in Williams’ box, and Zendaya, and some 23,000 other very partial observers at Arthur Ashe Stadium.

“There’s still a little left in me,” she said on the court when it was done.

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“I love a challenge, I love rising to the challenge.”

Williams will face unseeded Ajla Tomljanovic in the third round on Friday.

No matter who prevailed, this was never going to be a match with much subtlety. It was a showdown between two players who, when they are on, are among the best ball-strikers in the world, and two players at the opposite ends of the sport.

One of them, (assuming she keeps her word), was playing to extend the greatest career in modern tennis.

The other was attempting to get one thing that every young player wants — the chance to tell her grandchildren that in the biggest stadium in the sport, she beat the greatest player of all time.