Taking on the Japanese player on a breezy Philippe Chatrier, world number one Alcaraz won the first set easily only for his opponent to fight back at the start of the second.
It proved only a temporary blip, though, as the young Spaniard dominated the final two sets in a 6-1 3-6 6-1 6-2 triumph.
“I’m really happy with the level that I played today,” said Alcaraz. “I overcame the problems in the match because of the wind and it has been a really complete match from my side, and I’m really happy with that.”
Alcaraz’s positive attitude and sunny disposition has made him not just popular with his rivals but also made some of them rethink their own approach, with Stefanos Tsitsipas thanking the Spaniard during a practice session.
“I’m winning all the time because I am smiling,” said Alcaraz, who next faces Denis Shapovalov. “And I always said that smiling for me is the key of everything.
“I enjoy being in this kind of stadium, these kind of tournaments, cities. That’s the most important thing for me to enjoy, and that’s why I smile all the time.”
Tsitsipas joined Alcaraz in the third round with a 6-3 7-6 (4) 6-2 victory over Roberto Carballes Baena but former champion Stan Wawrinka lost out in the match of the day, going down in five sets to Thanasi Kokkinakis.
The Australian would have felt that was justice after his epic defeat by Andy Murray at his home grand slam in January.
“It definitely feels better when you come out on the winning end of those,” said Kokkinakis.
“I had a heart-breaker against Andy earlier in the year and not many moral victories. It was a tough one to take. You can’t count these guys out no matter how old they are. They get better and better, and you can see why they are multiple grand slam champions.
“Stan is a legend. Still is, obviously, but he was a legend out on court today. He was very nice, very respectful. Hats off to him. The crowd was going nuts for him, but it’s a fun atmosphere. I love playing against that, so it was awesome.”