The fourth seed was defeated in the third round 4-6, 7-6 (7/1), 6-4 by the 28th seed after being a break up in the deciding set.
The event has been tough on the big names at Roland Garros, with Jannik Sinner and Novak Djokovic crashing out of the men’s draw earlier.
“I think I’ve had a few (big wins) before, but I’d put it top three for sure,” Potapova said on court after earning a career third win over Gauff.
Despite losing her first service game to open the match, Gauff struck back to break the Russian-born Austrian in the eighth and 10th games and take the lead.
Potapova responded with two consecutive breaks of her own to race 3-0 ahead at the start of the second frame.
The 25-year-old’s serve then deserted her as well, as the next five games all produced breaks, with Potapova passing up two set points behind her own delivery.
Gauff responded to that reprieve by earning her first hold of the set to force Potapova to serve again for the frame.
The two-time major winner broke the world number 30 to level at 5-5 before holding again.
But Potapova then refound her own serve to force a tie-break.
A double fault dropped Gauff 5-0 behind, before she finally got on the board when Potapova overcooked a backhand.
It was too little, too late, however, as the Austrian powered to the next two points and sent the match into a deciding set.
Gauff drew first blood in the decider, pouncing on Potapova’s serve in the third game to nose in front, before being pegged back to 3-3.
A double fault in the next game brought Gauff two break-back points, but gutsy play allowed Potapova to hold.
A booming backhand winner down the line and a miss-hit Gauff forehand from deuce put Potapova 5-4 ahead with the world number four serving to keep her title defence alive.
But from 30-0, Gauff quickly unravelled and Potapova fell on her back in celebration as the American returned long and departed the tournament.
Potapova will meet Russian 22nd seed Anna Kalinskaya for a spot in the quarter-finals. (AFP)