NEW YORK -- When Caroline Wozniacki finished off the biggest victory of her still-fresh comeback following 3 years away from tennis, she sat in her US Open sideline chair, leaned forward and covered her face with both hands. Then she leaned back, glanced over at her husband and her father in the stands and smiled.

Two gold chains dangled from her neck, each carrying a name written in cursive: Olivia, for her 2-year-old daughter, and James, for her 10-month-old son.

Wozniacki clearly made the right choice to come out of retirement and try her hand at this tennis thing again, making it to the third round at Flushing Meadows by beating two-time Wimbledon champion Petra Kvitova 7-5, 7-6 (5) in Arthur Ashe Stadium on Wednesday night.

"This couldn't be better," Wozniacki said. "It's a dream come true. If you had asked me three years ago, I would have said I'll never be back here, playing on this court."

The 33-year-old from Denmark won the 2018 Australian Open and reached No. 1 in the rankings during her first stint on tour. Wozniacki left the sport in early 2020 to start a family with her husband, former NBA player David Lee, and later spent time working as a TV analyst.

Currently No. 623 in the world, she returned to competition this month and now is back at Flushing Meadows for the first time since 2019.

Wozniacki was the runner-up at the US Open in 2009, when she lost to Kim Clijsters in the title match, and 2014, when she lost to her good friend Serena Williams.

"I love New York. I love this court. I love everything about this city and playing here," said Wozniacki, who said she planned to hang out with her kids on Thursday. "Absolutely, as soon as I came here over a week ago, I already -- instantly -- felt so comfortable on these courts and knew that I could play some great tennis and I would be dangerous in the draw."

Next up will be a match against 2020 US Open semifinalist and 2021 Australian Open finalist Jennifer Brady, an American who recently came back to the tour after two years off because of injuries.

This is the third event of Wozniacki's comeback and she looked quite capable of strong play in her 15th career matchup against the 11th-seeded Kvitova. There were some wobbles, including when Wozniacki held her first two match points at 5-4 in the second set and failed to convert either.

But her game was good enough to hang in there and pull out the tiebreaker.

"Obviously we knew each other's game very well," Wozniacki said, "but I'm just so happy that I was the one who came out on top today."

Wozniacki now has 122 major match wins in her career, the fourth-most among active women behind Venus Williams, Victoria Azarenka and Kvitova, according to ESPN Stats & Information research.

The Associated Press contributed to this report.