Williams will open her doubles match with her sister Venus on Wednesday.
Williams will face world number two Anett Kontaveit of Estonia in the 64 singles round, also on Wednesday. It will be their first job meeting.
After early struggles with her serve on Monday night, Williams has made 10 of her last 13 matches against Kovenic, the 27-year-old from Montenegro and ranked 80th in the world.
After the match, during a party celebrating her tennis career, Williams said she received a boost from the vocal crowd of nearly 24,000. “The crowd was crazy,” she said.
Williams double-faulted in the first half but eventually raised her first serve percentage to 66%. She won 33 out of 43 serving points.
The defining moment came in Game Six of the first set when Kovinic looked on the verge of a 4-2 lead. But Williams’ shot that looked long and wide was not, chomping at the back of the baseline and the outer edge of the singles sideline. This was Williams’ first 11 consecutive points and she sprints the rest of the way.
It was Williams’ third match since she announced that she would “evolve away from tennis”.
“I never liked the word retirement. It doesn’t feel like a modern word to me. I’ve been thinking of this as transition, but I want to be sensitive about how I use that word, which means something very specific,” Williams said in a Vogue article earlier in the day. This month is “important to a community of people”.
“Probably the best word to describe what I’m up to is development,” she said. “I’m here to tell you that I’m developing away from tennis, toward other things that are important to me.”
At her post-match press conference, she was asked if this was definitely her last tournament.
“Yeah, you were pretty vague about that, right?” She said with a smile. “I’ll keep it a mystery because you never know.”
But earlier in court, Williams, 40, said it was a tough decision moving forward.
“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 hard to get away from not doing it. That was the case for me.”
When Gayle King asked her what it would be like to win in the future, Williams referred to her venture capital firm and also said she wanted to work on her spiritual life.
Williams’ singles win saw her husband, Alexis Ohanian, and their daughter Olympia, as the young woman wore white beads in her hair, reminiscent of Williams’ appearance when she won her first of six US Open titles as a teen in 1999.
“I’m looking forward to getting up and being like, OK, I don’t have to run to court today,” Williams said. “I am looking forward to being just a mother. She is a good girl. I just want to be a good mother to her.”
Also on Monday, Ukrainian Daria Snegur, who won qualifying matches to reach the tournament, beat Romania’s No. 7 Simona Halep in three sets 6-2, 0-6, 6-4.
“This match is for Ukraine, for my family, for all the fans who supported me. I want to say thank you to all of you,” said the emotional Snygor.
It was the first ever Grand Slam match for Snegur at this level. She won the women’s singles Wimbledon title in 2019.
CNN’s Jill Martin contributed to this report.
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