The 17-year-old secured the win over the Tunisian with a dominant serving match, losing just nine points on her own serve in the two-set encounter.
Gauff’s win over Jabeur came after she also enjoyed a quick match in the previous round, with her opponent, Australian Open finalist Jennifer Brady, retiring with an injured left foot after Gauff won the opening set.
The American, who won the junior title at Roland-Garros three years ago, is yet to drop a set in singles.
Gauff will next face Barbora Krejcikova, who also reached reached her first quarterfinal at a major by beating 2018 French Open runner-up Sloane Stephens 6-2, 6-0.
Krejcikova saved all three break points she faced while Stephens ended up with 26 unforced errors.
Krejcikova won her first WTA title in Strasbourg in the buildup to the French Open. She reached the fourth round at Roland Garros last year.
Stephens won the U.S. Open in 2017 had her run to the final at the French Open the next year.