Seventeen-year-old Gauff played compatriot Jennifer Brady but secured swift passage to round four as her opponent was forced to retire because of injury.
The teenager had produced a ruthless, relentless 19-minute opening set, winning 6-1 before Brady called a medical timeout.
She quickly made the call to withdraw, allowing Gauff to move on and continue her best run at a tournament she won as a junior in 2018. Ons Jabeur is next.
Gauff will be among four Americans in the last 16 after 2020 finalist Sofia Kenin came from behind to beat another compatriot in Jessica Pegula in three sets. Sloane Stephens overcame No.18 seed Karolina Muchova in two.
There had been eight players from the United States in the third round at Roland Garros, with only Madison Keys – beaten by Victoria Azarenka on Saturday (AEST) – losing to a foreign opponent.
Stephens said: "I think obviously American women tennis is in a really great place. I think we all are having good results and everyone is playing well.
"Obviously, it's different. I think we're all friends. We're all very friendly. We all support each other. We all love seeing each other do well, which I think is really nice.
"It's great to have so many players in the top 100, just because we're just a super strong nation right now.
"I think that's also a very cool, super strong Fed Cup team. Everything that you would think of, we have, so I think that's really cool."
Stephens will face Barbora Krejcikova next after she claimed the day's biggest scalp, defeating No.5 seed Elina Svitolina 6-3 6-2.
Krejcikova identified an epic battle at 4-3 in the opener as the "key game", staving off four break points to hold.
On Svitolina's serve, the Czech converted six of 13 opportunities and, despite breaking in the very first game, felt she improved as the match wore on.
"It was really tough because also I didn't know Elina that well," Krejcikova said. "I never played her, I never practiced [with] her.
"So I didn't really know, I wasn't really sure what kind of ball I should expect. I felt weird.
"But as the match went on and I was playing and playing, I just started to feel better, and actually at the end I was just feeling really well and I was just going for my shots."
Kenin has Maria Sakkari in the fourth round after her win over Elise Mertens, but the American could be excused for already having one eye on a potential quarter-final.
She is on course to meet defending champion Iga Swiatek, who beat Kenin in last year's final and is in supreme form again in 2021.
Anna Kontaveit broke Swiatek in the opening game of their clash but could not protect her advantage and was edged in a tie-break.
That set the stage for a devastating display of Swiatek's talent in which she claimed a bagel with only a single unforced error.
Despite the dominant nature of the second set, the Pole said: "It's good to have matches like that because it keeps you down to earth and you have to just be careful on every point and on every game."