Potapova rattled Gauff with powerful baseline hitting and broke to love in the opening game, before taking a 4-2 lead when the American slipped and dropped to the floor of Court Philippe Chatrier while trying to reach for the ball.
In a brutal couple of days for the fancied players at Roland Garros, with Jannik Sinner and Novak Djokovic crashing out of the men's draw, Gauff was unable to find her best level when it mattered most and joined the scrap heap of stars.
Her premature exit leaves four-times champion Iga Swiatek and world number one Aryna Sabalenka as the leading contenders to claim the trophy, while Potapova will fancy her chances as the dark horse having dished out a massive upset.
"I'm cramping a little bit, but it's OK, it's all good. I don't have any words now, I'm extremely happy," Potapova said in her on-court chat as she clutched her right arm after two hours and 37 minutes of big hitting.
"The fight we could show, both of us... Coco's such a champion and I respect her so much. I'm unbelievably proud of myself that I stayed there, that I was fighting until the very last point."
Potapova rattled Gauff with powerful baseline hitting and broke to love in the opening game, before taking a 4-2 lead when the American slipped and dropped to the floor of Court Philippe Chatrier while trying to reach for the ball.
Gauff dusted herself off and won the next two games in front of a sparse centre court crowd, with the attention split between Paris St Germain's Champions League soccer final with Arsenal in Budapest and Frenchman Moise Kouame in action at Roland Garros.
The 22-year-old raised her game again to take the first set, but Russian-born Potapova immediately ramped up the pressure and targeted the American's wobbly serve to grab a double break at the start of the second set.
Potapova was on the verge of levelling the match while ahead 5-2 but Gauff moved through the gears to surge ahead by claiming four games in a row, only to lose the next game and then the set in a tiebreak where her serve let her down.
The pair traded breaks in a breathless decider, but world number four Gauff lost her way as Potapova took control and went through in style for a meeting with 22nd seed Anna Kalinskaya in the fourth round.
Potapova, ranked 30th in the world, said it was one of the biggest wins of her career.
"It's up there in the top three for sure," she added.
