In a performance described by former British No.1 Tim Henman as "an absolute clinic", Alcaraz swept to a 6-4 6-4 6-2 win against American Sebastian Korda.
Korda, 21, is widely expected to be a star of the men's tour for years to come, and he beat Alcaraz on clay in Monte Carlo only last month.
This time he found 19-year-old Spaniard Alcaraz too hot to handle on the surface, with the fast-rising world No.6 demonstrating the form that has brought him an ATP Tour-leading four titles in 2022 already.
Tournament organisers were giving the Paris crowds a glimpse into the future by handing Korda and Alcaraz the hot-ticket night session slot. They are both becoming increasingly a factor in the present, too, and Alcaraz is rated a strong contender for the title this fortnight.
Victory made him the youngest man to reach round four at the French Open since Novak Djokovic in 2006, the ATP said. After winning titles in Barcelona and Madrid, Alcaraz is on a 13-match winning run.
It took him two hours and six minutes to get the job done this time, flashing 18 passing shot winners past his opponent, the son of one-time Roland Garros runner-up Petr Korda.
"It's amazing to play in front of such a great crowd, a great atmosphere here in Philippe-Chatrier," Alcaraz said. "I think the night session is fun to play, the whole people enjoyed the match, and I'm grateful to play in front of such a good crowd.
"Of course, in early matches I'm trying to have fun out there. I love playing this kind of tennis court. I love playing in France. I'm enjoying every single second."
Baseliner Alcaraz surprised many by bringing out a rush of serve-volley points, and revealed that was at the behest of coach Juan Carlos Ferrero.
He also revealed how Ferrero, who was briefly a world No.1 and won the 2003 French Open men's title, remained in great nick on the practice courts at the age of 42.
"I think not too far away, a couple of months ago or a year ago, he beat me in a training set," Alcaraz said. "He's in good shape, and he could beat a lot of players now in a training set."
Henman, analysing the match for Eurosport, said Alcaraz was the complete package. It was a performance that suggested Alcaraz's five-set struggle against Albert Ramos-Vinolas in round two was a blip.
"I thought his performance was absolutely incredible," former world No.4 Henman said. "Korda perhaps didn't play as well as he would have liked, but he wasn't allowed to play because of the sheer quality of Alcaraz in every area.
"All credit to Alcaraz, it was an absolute clinic out there."
Henman said the youngster turned "defence into attack in the blink of an eye", adding: "I think he came in expecting a really difficult match, and he destroyed Korda."
Alcaraz reached the third round on his Roland Garros debut last year, and has now gone a step further, with Russian Karen Khachanov awaiting him next.
Swedish great Mats Wilander, who won the French Open three times in the 1980s, said Alcaraz on the backhand was "very much like Novak Djokovic".
"The forehand side I'm not really sure, I can't explain it," said Wilander, "because the speed of his arm and when he decides to go full... when he goes full it is unbelievable when the ball hits the clay and bounces."