Alcaraz celebrates 100th Slam match with easy win at Australian Open
The 22-year-old six-time major winner was at a different level on Rod Laver Arena to book his passage 6-2, 6-4, 6-1 in 2hrs 5mins.
Victory thrust him into a clash for a place in the quarter-finals with American 19th seed Tommy Paul, who progressed when Spanish opponent Alejandro Davidovich Fokina retired hurt.
Alcaraz has never gone past the last eight in his four previous trips to Melbourne Park, with the Australian Open the only Grand Slam missing from his burgeoning collection.
He will become the youngest man to win all four majors should he push on and make his breakthrough.
"It wasn't easy. To be honest, when you play someone like Corentin you don't know what's going to be next," said the Spaniard.
"So that's really difficult, you know, to approach the match. But I had fun on the court. I think we both pulled off great shots, great points."
The win against Moutet came in his 100th Slam match with Alcaraz having a remarkable 87-13 win-loss record -- matching the legendary Bjorn Borg at the same stage of his career.
Left-hander Moutet had never beaten a world number one and never looked like doing so on centre court.
Top seed Alcaraz was quickly into his stride, breaking Moutet in the opening game before holding for 2-0.
The Frenchman got into gear with a hold in the third game, but was largely a bystander as Alcaraz raced through the set in 35 minutes.
An immediate break for Alcaraz set the tone for the second set. But Moutet reeled off four straight games from 0-3 down, throwing in some underarm serves, dropshots and tweeners for good measure.
Alcaraz steadied and took the set before barely breaking a sweat in the third.