The 18-year-old Gauff, the youngest remaining woman in the draw, defeated the 36-year-old Kanepi, the oldest remaining woman, 6-3, 6-4.
The young American is trying to improve on her quarterfinal run at Roland Garros a year ago.
Gauff had six aces — and five double-faults — while her Estonian opponent made 29 unforced errors. The teenager has not dropped a set in her first three matches.
Leylah Fernandez Beats Belinda Bencic
U.S. Open runner-up Leylah Fernandez has reached the fourth round at the French Open for the first time.
The 19-year-old Canadian beat Olympic gold medalist Belinda Bencic 7-5, 3-6, 7-5 at Court Philippe Chatrier.
The 17th-seeded Fernandez broke Bencic in the 11th game of the deciding set and served out the match. She had saved two set points in the opener.
Fernandez next faces 20-year-old Amanda Anisimova, who reached the Roland Garros semifinals in 2019.
The best result by a Canadian woman at the French Open was Eugenie Bouchard making the semifinals in 2014.