Williams will open doubles play with her sister Venus on Wednesday.
Williams will face world No. 2 Anett Kontaveit of Estonia in the singles round of 16, also on Wednesday. It will be his first career meeting.
After early struggles with her serve on Monday evening, Williams won 10 of her last 13 games against Kovinić, a 27-year-old from Montenegro who is ranked 80th in the world.
After the match, during a ceremony celebrating her tennis career, Williams said she got a boost from the vocal crowd of nearly 24,000. “The crowd was crazy,” he said.
Williams double-faulted in the first game, but eventually increased her first serve percentage to 66%. He won 33 of 43 first serve points.
A key moment came in the sixth game of the first set, when Kovinić came close to serving at 4-2. But a shot from Williams that looked long and wide was neither, clipping the back of the baseline and the outside edge of the singles sideline. It was the first of 11 straight points for Williams as she went the rest of the way.
It was Williams’ third match since announcing she will “evolve away from tennis.”
“I’ve never liked the word retirement. It doesn’t feel like a modern word to me. I’ve been thinking about it as a transition, but I want to be sensitive about how I use that word, which means something very specific and important to a community. of people,” Williams said in a Vogue article published earlier this month.
“Maybe the best word to describe what I’m doing is evolution. I’m here to tell you that I’m evolving away from tennis, towards other things that are important to me,” he said.
In his post-match press conference, he was asked if this is definitely his last tournament.
“Yeah, I’ve been pretty vague about it, haven’t I?” she said with a smile. “I’ll stay idle because you never know.”
But earlier on the court, Williams, 40, said it was a difficult decision to move on.
“I think when you’re passionate about something and you love something so much, it’s always hard to walk away,” he said. “Sometimes I think it’s harder to leave than not. That’s been the case for me.”
When asked by Gayle King what the future holds for her, Williams pointed to her venture capital firm and also said she wants to work on her spiritual life.
Williams’ individual victory was witnessed by her husband, Alexis Ohanian, and daughter, Olympia, with the young woman wearing white pearls in her hair, reminiscent of Williams’ appearance when she won the first of her six WTA titles. US Open as a teenager in 1999. .
“I feel like waking up and being like, OK, I don’t have to run on the track today,” Williams said. “I’m looking forward to just being a mom. She’s a good girl. I just want to be a good mom to her.”
Also on Monday, Ukraine’s Daria Snigur, who won her qualifying matches to enter the tournament, cruised past No. 7 seed Simona Halep of Romania in three sets 6-2, 0-6, 6-4.
“This match for Ukraine, for my family, for all the fans who supported me. I want to thank you all,” said an emotional Snigur.
It was Snigur’s first Grand Slam match at this level. She won the Wimbledon women’s singles title in 2019.
CNN’s Jill Martin contributed to this report.