Williams opens the doubles with her sister Venus on Wednesday.
Williams will face the world No. 2, Estonia’s Anett Kontaveit, in 64’s singles, also on Wednesday. It will be their first career meeting.
After an early struggle with her serve Monday night, Williams took 10 of their last 13 games against Kovinić, a 27-year-old from Montenegro who is 80th in the world.
After the match, at a ceremony honoring her tennis career, Williams said she got a boost from the vocal crowd of nearly 24,000 people. “The public was crazy,” she said.
Williams made two double faults in the first game, but eventually increased her first serve percentage to 66%. She won 33 of the 43 first service points.
A key moment came in the sixth game of the first set when Kovinić was about to take a 4-2 lead. But a shot from Williams that looked long and wide was neither, cutting the back of the baseline and the outside edge of the singles sideline. It was the first of 11 straights for Williams as she kissed the rest of the way.
It was Williams’ third game since announcing that 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 considered this a transition, but I want to be sensitive to 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.
“Perhaps the best word to describe what I’m up to is evolution. I’m here to tell you that I’m evolving from tennis into other things that are important to me,” she said.
At her post-match press conference, she was asked if this is definitely her last tournament.
“Yeah, I’ve been pretty vague about it, haven’t I?” she said with a smile. “I’m staying vague, because you never know.”
But earlier in court, Williams, 40, said it was a tough 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,” she said. “Sometimes I think it’s harder to walk away than not to. That’s been the case with me.”
When asked by Gayle King what winning will be for her in the future, Williams pointed to her venture capital firm and also said she wants to work on her spiritual life.
Williams’ win in singles was watched by her husband, Alexis Ohanian, and their daughter, Olympia, with the younger wearing white beads in her hair, reminiscent of Williams’ appearance as she won the first of her six US Open titles. won as a teenager in 1999 .
“I’m looking forward to waking up and just saying, okay, I don’t have to run to court today,” Williams said. “I’m looking forward to just being a mom. She’s such a good girl. I just want to be a good mom to her.”
Also on Monday, Daria Snigur of Ukraine, who won qualifiers to enter the tournament, upset number 7-seeded Simona Halep of Romania in three sets 6-2, 0-6, 6-4.
“This game for Ukraine, for my family, for all the fans who have supported me. I want to thank you all,” said an emotional Snigur.
It was Snigur’s first ever Grand Slam match at this level. She won the Wimbledon title in girls’ singles in 2019.
CNN’s Jill Martin contributed to this report.