The German, fired up by a code violation for being coached from the stands by his father, stormed into the lead in the fourth set before securing victory in 3-1/2 hours on Court Suzanne Lenglen.
It is the first time Zverev has reached the quarter-finals of a Grand Slam and he will face Austrian seventh seed Dominic Thiem, who beat Japan’s Kei Nishikori 6-2 6-0 5-7 6-4.
Nishikori took his only break point opportunity to claim the third set but Thiem, twice Roland Garros semi-finalist, regained control in the fourth.
Former champion Novak Djokovic never looked in trouble as he booked a 12th quarter-final appearance in Paris with a 6-3 6-4 6-2 win over Spanish veteran Fernando Verdasco.
US Open runner-up Madison Keys advanced to the last eight without dropping a set, defeating Romania’s Mihaela Buzarnescu 6-1 6-4.
Up next for Keys is Kazakh Yulia Putintseva, who upset 26th seed Czech Barbora Strycova 6-4 6-3.
Sloane Stephens sprinted past Estonian Anett Kontaveit 6-2 6-0 to set up a potential semi-final meeting with Keys, whom she beat in last year’s US Open final.
