The second-seeded American, pursuing her first title at Roland-Garros, eliminated 172nd-ranked qualifier Tereza Valentova, of the Czech Republic, 6-2 6-4 in 75 minutes
It followed her 6-2 6-2 first-round victory against Australia's world no. 91 Olivia Gadecki.
Gauff, the 2023 US Open champion, only managed to produce 11 winners, five fewer than her far less experienced opponent. Gauff also finished with 23 unforced errors, a total that included a half-dozen double-faults.
Against Valentova, an 18-year-old who won the junior title at the French Open last year and was competing in the main draw at a major tournament for the first time, Gauff got broken five times.
Four of those came in the second set but each time, the 21-year-old Floridian managed to immediately rebound to claim Valentova's next service game.
"There is a sense of urgency after getting broken, for sure. You don't want to get too far behind. You don't want to get two breaks down. You can live with one break. But she's definitely got to serve better and do a better job of holding as the tournament progresses," said Gauff's father, Corey.
"She's probably been one of the best returners of serve on the tour the last two to three months. But that's not what you want. You want to hold first, for sure. It's not really a break until you hold."
Gauff, the 2022 runner-up, will now try to reach the fourth round in Paris for the fifth consecutive time on Saturday, when she faces another Czech player, Marie Bouzkova.
Elsewhere, Spanish 10th seed Paula Badosa came from a set down to beat Romania's Elena-Gabriela Ruse 3-6 6-4 6-4 to advance to the third round, where she will face either Australia's 17th seed Daria Kasatkina or French wildcard Leolia Jeanjean.
Australian Open champion Madison Keys, seeded seventh, dispatched Britain's Katie Boulter - who smoothed her opponent's path with nine double faults - 6-1 6-3 to set up a third-round tie with fellow American Sofia Kenin, who tipped out Victoria Azarenka 7-6 (7-5) 6-4.
American third seed Jessica Pegula overcame compatriot Ann Li 6-3 7-6 (7-3) to earn a third-round clash with the Czech Republic's unseeded 2019 Paris finalist Marketa Vondrousova, who eliminated 25th seed Magdalena Frech 6-0 4-6 6-3
Russian sixth seed Mirra Andreeva beat American Ashlyn Krueger 6-3 6-4.
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