The American, 19, had to fight back from a break down in the third set to win 6-3 3-6 6-1.
Gauff, the sixth seed, is vying for his first Grand Slam victory.
The triumph also marked the end of Wozniacki’s remarkable comeback after a three-and-a-half-year sabbatical from the sport.
Gauff came into her home Grand Slam with a lot of confidence after winning titles in Washington and Cincinnati.
Her good form appears to be continuing, as she fought back in the third set to win a remarkable match against a tenacious Wozniacki.
Gauff later joked that her father can’t sit in her support box anymore because he gets too nervous during games.
“He’s been doing laps around the stadium,” she revealed.
“I don’t know if he can hear me, but I felt his good energy even though I couldn’t see him.”
Gauff’s next opponent will be either defending champion Iga Swiatek or former French Open winner Jelena Ostapenko.
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Gauff, who was broken in her first service game, recovered to equalize the scores at 2-2 before taking the key break to lead 5-3 and serve out the opener on the third set point.
Despite saving five break points in the second set, Gauff eventually dropped service to trail 5-3 and allow Wozniacki to advance to the fourth round.
onto the start of the third quarter, the girl experienced another breakdown and turned her rage onto her coaching staff, yelling at them to stop talking to her.
The home favorite channeled her energy brilliantly, overcoming the deficit and breaking Wozniacki to take control of the match, while the audience inside Arthur Ashe Stadium screamed her on.
Gauff has lost just one of her last 16 matches since her unfortunate first-round departure at Wimbledon in July, and she is now on a nine-match winning streak.
The world number six has only reached one Grand Slam singles final, the 2022 French Open, when she was defeated by Swiatek 6-1, 6-3.
If the Pole wins Ostapenko later on Sunday, Gauff might face the top seed in the quarter-finals, but former British number one Annabel Croft believes the American has “put herself in the best possible position” to beat Swiatek.
“I believe this was an excellent test for her. “She had to fight hard and be physical,” Croft noted.
“She had to go toe-to-toe with me, and I think the quality of the tennis and ball striking was phenomenal.”
