NEW YORK — American razzmatazz filled the air, speakers spoke, singers sang, flags appeared, two star players emerged to big cheers, and then the Monday evening program turned to the real formality.

One of the greatest non-rivalries in sports history resumed in Arthur Ashe Stadium at the U.S. Open, and it played its long-standing tune. In a first-round match in the shiniest nook of the draw, 23-time Grand Slam winner Serena Williams, 37, destroyed five-time Grand Slam winner Maria Sharapova, 32, just as Williams generally does.

Her 19th consecutive win over Sharapova, a string that began at the 2005 Australian Open and lays strewn across 15 tennis seasons, counted as an annihilation among annihilations. The final score, 6-1, 6-1, meant Williams has won 20 of their 22 matches together and 38 of their past 40 sets. Two of those 38 sets have gone 6-0, and 13 more have gone 6-1.

Soon, very soon, Williams was off to the second round in her continuing hunt to become the second player to win 24 Grand Slam singles tournaments and the fourth to win any after giving birth, where she would join Australia’s Margaret Court in both categories. Next up comes Cincinnatian Catherine McNally, who at No. 121 in the world pulled rank on the former top-10 player at No. 89, Timea Bacsinszky of Switzerland, 6-4, 6-1. That set up a meeting between a 37-year-old (Williams) and a 17-year-old (McNally), who is the same age Sharapova was when, in 2004, the Russian took a 2-1 lead in the series with Williams before the long, uncommon deluge to 2-20.

“Gosh,” Williams said, when reminded of the 19 straight matches and the 15 long years. “I never thought about it like that.”

In an explanation Williams uttered matter-of-factly, without a trace of gloat, she gave partial credit to a quirk when she said, “I just feel like her game really matches up well against mine. I always said her ball somehow lands in my strike zone. I don’t know. It’s just perfect for me.”

It seems Sharapova can “win” only when Williams proves unable to appear, as happened at the second Monday of the 2018 French Open, when Williams withdrew before their meeting because of an arm injury that left her unable to serve, which may or may not have proved a detriment. Such walkovers don’t count in the official head-to-head.

Still, the crowd showed up and the U.S. Open sanctioned its first Williams-Sharapova meeting. The players appeared on the stadium video screen as they headed down the hallway to the court, and Williams, making her first appearance since the mighty kerfuffle that decorated her 2018 final against Naomi Osaka, gained some oomph from the sound.

“I could hear them [while] walking down the hallway,” she said. “It was such a good feeling. It made me feel unbelievable, really helped me get amped up and pumped up.”

Then it began, because apparently it must. Fifteen years and five months after their first meeting in Miami, and 15 years and two months after their Wimbledon final that became a Sharapova upset romp, they helped each other warm up yet again. They had had similarly spare seasons, Williams playing only 24 matches, Sharapova 14. Williams had withdrawn four times, with back spasms forcing the issue after four games of the first set of the final in Toronto on Aug. 11, her most recent appearance. “Yeah, back feels good,” Williams said later.

Williams held serve impressively. Sharapova held serve for 1-1 and looked excited, even if onlookers with knowledge of the gigantic trend might have wondered why. Once Sharapova led 30-15 while serving at 1-2, however, things started to look familiar. Her game began leaking beneath the superior power and variety of that of Williams, whose screaming shots repeatedly visited corners and wreaked errors from Sharapova.

After 17 minutes, it was 4-1. After 22 minutes, it was 5-1. After 24 minutes, it was 6-1. Williams had won 15 of the last 17 points of the first set, and the statistics read like a benign graveyard: 27-12 in points, 3-10 in unforced errors, 6-8 in forced errors. A mild ripple hit the second set when Williams faced two break points while serving at 2-1, but Williams cleaned up that little spot largely with a backhand passing shot that wowed the crowd and a driving forehand into the corner all full of higher caliber.

Somebody asked if that turn made the match seem closer. Sharapova replied that it did not. Williams credited Sharapova’s renowned pugnacity but then took a mid-sentence trip back to the reality of the match when she said, “One point here or there, she could have won at least another game.”

No rally exceeded 12 shots. On rallies of zero to four shots, Williams won 39 of 60 points. Snippets of sympathy began to turn up in the audience even as the crowds here clearly intend to back the seeker of tennis history.

After 59 minutes, it concluded. After an ordinary handshake, Sharapova departed hurriedly and Williams thanked the crowd. Later, Williams fielded a question about the United States Tennis Association’s decision to refrain from having Carlos Ramos umpire any of her matches after their set-to last year, with, “Yeah, I don’t know who that is.”

“Bottom line is I believe in my ability,” said Sharapova, whose eight Grand Slam appearances since her return in 2017 from a performance-enhancing-drugs suspension have yielded just one quarterfinal, and that one attained after Williams withdrew. “You can write me off. There are many people that can write me off, especially after going down, 6-1, 6-1, in the first round of the U.S. Open.

“As long as it’s not the person inside of you, you’ll be okay.” As long as the person opposite the net isn’t Williams, she just might be.

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