Gauff, who is playing at a Grand Slam tournament for the first time, won 3-6, 7-6 (7), 7-5 on Centre Court.
Gauff has won both her Wimbledon matches in straight sets to set up a meeting with Polona Hercog in round three.
Tennis fans leapt to their feet, cheered and applauded after 15-year-old Gauff, known as Coco, fought off two match points to beat Polona Hercog on Friday evening.
"I remember before I played Venus", Gauff recalled at her post-match press conference, "one little kid asked for a picture and then after the next day, after I played Venus, everyone was screaming my name so it's just pretty surreal how life changes in a matter of seconds".
She has become the youngest female player in the history of tennis who had made it to the third round successfully in Wimbledon Championship since American star Jennifer Capriati who reached the semifinals of the tennis tournament in 1991.
Gauff had a brief chat with Roger Federer before the match, and the eight-time victor will have no doubt approved as two superb serves got her out of a mild sticky patch for 4-2. She defeated Viktoria Kuzmova in round one of Wimbledon and 16th ranked Madison Keys in round two. Hercog came back out; play eventually resumed; and, despite a sixth double fault, Gauff held serve to calm the nerves and ease herself into the match-winning set.
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Gauff will face Simona Halep in the fourth round.
"I think I can beat anyone who's across the court", Gauff said after Wednesday's win.
During a late changeover in a mixed doubles match on Court 15, the sprinkler behind the chair umpire sent water gushing behind the backs of New Zealand's Artem Sitak and his aprtner Laura Siegemund.
"Against Halep it will be tricky - the pressure is all on her as a big favourite, but the crowd will be going nuts for Gauff which will be hard for the Romanian to handle". The momentum carried over with Gauff leading 4-1 in the third, only for Hercog to get to 4-4. He then broke for a 2-1 lead in the fourth and sealed the victory with a service victor on his first match point.
This was her Centre Court debut, but the crowd soon took her to their hearts, even before her impressive comeback. The Pole, ranked world No. 48, narrowly lost the first set 5-7 before taking the second in a tiebreak.
Gauff faced two match points in the second set.
They played for over an hour. "Everyone knows who she is and she is on target right now, for sure, to become the best tennis player in the world".