Fifth-seeded Argentine Juan Martin del Potro booked his place in the last 16 at Roland Garros for the first time in six years, with a straightforward 7-5 6-4 6-1 victory over Spain's Albert Ramos-Vinolas.
It promises to be a hard-hitting match, with big serves and booming forehands, when Isner meets del Potro in the fourth round.
"After a few days, I tried to get an autograph", she said. This match-up completely suits the Spaniard, because the one-handed backhand can be vulnerable with heavy top-spin on a clay court and Nadal also plays well against players that give up a lot of ground in the baseline exchanges.
Nadal, who is yet to lose a set from his opening three rounds, will next face Maximilian Marterer after the German had earlier defeated lucky loser Jurgen Zopp 6-2 6-1 6-4. "It has been three hard matches for me, but I played well and I know I could play even better in my next round", del Potro said.
"What I know is I go to the court, and I know that I can win, I can lose".
He has won 12 consecutive matches at Roland Garros; the last loss was against Novak Djokovic in the 2015 quarterfinals.
"He hits the ball with big topspin", Nadal said. The pair were regarded as two of the best young players of their generation as juniors, but Nadal has won 16 Grand Slam titles while Gasquet has never reached a final at the majors. "He has power, so he's a risky opponent", said Nadal.
No. 3 Marin Cilic eliminated Steve Johnson of the United States 6-3 6-2 6-4.
With about a week to go, Nadal is looking more and more like the absolute favorite. Stephens next faces Anett Kontaveit of Estonia, who won 7-6 (6) 7-6 (4) against No. 8 seed Petra Kvitova.
In another rain-affected game, Belgian David Goffin (8th seed) saved four match points to defeat Frenchman Monfils in a thriller, 6-7 (6) 6-3 4-6 7-5 6-3.
Djokovic has been shaky at times, too.
Karen Khachanov inflicted more French woe by completing a rain-interrupted win over Lucas Pouille on Philippe Chatrier.
Should he and Fognini, who is also through to the round of 16 this year, both reach the quarterfinals, it will be the 2nd time in the Open Era that Italy has had multiple representatives in the quarterfinals of the men's singles at a Grand Slam.