Nadal beat Stefano Travaglia 6-1, 6-4, 6-0 in 95 minutes to continue his quest for a 13th singles title.
Wawrinka lost in five sets to the 20-year-old after just over three hours on Court Suzanne Lenglen.
When the 35-year-old Swiss levelled at two sets apiece, it appeared his greater experience might tell in the fifth set.
But he lost his serve at the start of the decider and did not recover.
Gaston, who was invited to play in the main draw despite his world ranking of 239, will play third seed Dominic Thiem in the last 16 after he advanced with a commanding straight sets win over the fast-rising Norwegian Casper Ruud.
The Austrian, beaten finalist in 2018 and 2019, wrapped up the 6-4, 6-3, 6-1 victory in two and a quarter hours under the roof on Court Philippe Chatrier.
“I’m very happy with my match,” said Thiem in his post-match interview with Cedric Pioline. "I made very few mistakes.”
Ruud, the 28th seed, has been one of the form players of the clay court swing. He reached the semi-finals at the Hamburg Open as well as at the Italian Open.
"Casper has a great attitude,” added the US Open champion. “He was fighting from the very first point right until the end. He was giving 100 percent and I did not want to give him any chances to think that he might be able to come back.”
