NEW YORK Serena Williams is not ready to say goodbye just yet. Nor, clearly, are her fans.

In her first match at what is expected to be the last U.S. Open — and last tournament — of her remarkable playing career, Williams overcame a shaky start to overwhelm Danka Kovinic 6-3, 6-3 on Monday night in a packed Arthur Ashe Stadium with an atmosphere more akin to a festival than a farewell.

Looking ahead to a future without tennis competition, Williams told the crowd: “There’s other chapters in life.”

Early, Williams was not at her best. Maybe it was the significance of the moment. There were double-faults. Other missed strokes, missed opportunities. She went up 2-0, but then quickly trailed 3-2. Then, suddenly, Williams, less than a month from turning 41, looked a lot more like someone with six championships at Flushing Meadows and 23 Grand Slam titles in all — numbers never exceeded by anyone in the professional era of tennis, which began in 1968.

She rolled through the end of that opening set, capping it with a service winner she reacted to with clenched fists and her trademark cry of “Come on!” The more than 23,000 in the stands (thousands of others watched on a video screen outside Ashe) rose for a raucous standing ovation — and did so again when the 1 hour, 40-minute contest was over, celebrating as if another trophy had been earned.

Instead, there is plenty more work to be done. Williams played in the second round of singles on Wednesday against No. 2 seed Anett Kontveit of Estonia. And there’s also doubles to come, too: Williams and her sister, Venus, are entered together in that competition, with their initial match slated for Wednesday or Thursday.

“Just keep supporting me,” Williams said, “as long as I’m here.”

There can be no doubt, the folks so enthusiastically backing Williams on Monday will come again to the U.S. Open from far and wide for Serena — no last name required, befitting someone as much an icon as superstar athlete — eager to see her play or, if not lucky enough to hold the right ticket, hoping for an autograph, a glance at her practicing or merely the chance to breathe the same Flushing Meadows air as her.

They were there to honor her and show appreciation for what she’s done on the court and off. After watching the victory over Kovinic, spectators held up blue, white or red placards that were distributed at their seats to spell out “We (Heart) Serena.”

While Williams did not exactly declare that the U.S. Open definitively would be her last hurrah, she has made it sound as if it will be.

Spike Lee participated in the pre-match coin toss. Former President Bill Clinton was in the stands. So were Mike Tyson and Martina Navratilova, sitting next to each other.

When Williams made the short walk to the practice courts beside Ashe Stadium for a half-hour hitting session to warm up before Monday’s match, people packing the bleachers above the practice area greeted her with shrieks of “Serenaaaaa!” on her way in, and again yelled on her way out, receiving a wave of her racket as acknowledgment before Williams strode, lips pursed, back into the stadium.

She means a lot to a lot of people. As a tennis player. As a woman. As an African-American. As a mother. As a businesswoman.

Her daughter, Olympia, who turns 5 on Thursday, wore white beads in her hair while sitting with her father and grandmother in the stands on Monday, a nod to her mom’s hairstyle when she won her first U.S. Open in 1999 at age 17.

“Once Serena announced she would play the U.S. Open, we sold out in a nanosecond for Monday night and Tuesday night. You can see on the secondary market, the get-in price is $230. I saw $5,800 for a courtside seat this evening. Look, this is a historic moment for the Williams family, for Serena and our sport,” said Stacey Allaster, the tournament director of the American Grand Slam event. “It is so difficult to really capture what Serena and Venus have done for the sport of tennis. They have transformed our sport. They’ve made us more inclusive. And they’ve transcended sports.”