Alcaraz enjoyed a dominant opening win over Flavio Cobolli in his first match as the top seed in a Grand Slam and he made another blistering start against Daniel to ease through the first set on the back of two breaks.
Daniel pounced early in the next to grab a 3-0 lead before Alcaraz got on the board. He continued to batter the suddenly error-prone Spaniard with relentless hitting from the baseline before levelling the match.
But the Japanese player, ranked 112th in the world, was on the back foot again on a gusty Court Philippe Chatrier as Alcaraz regained focus to break early in the third set and he closed out the win in style.
"I'm a player who plays really well in the wind. I have practised in Vienna which has a lot of wind, a lot of days and I'm used to playing in the wind," he said.
"It's really tough to adapt your game to that. I tried to play as best as I can. Today, I played a good level."
Alcaraz will next play Canadian 26th seed Denis Shapovalov.
"I've never played against him. But I practised in Barcelona with him. Everybody knows his level," Alcaraz told reporters.
"He's a really dangerous player. He has great shots. It's going to be a really difficult match. I have to be ready, really focused on his shots.
"I try not to think about the opponent. I try to think about myself, about my game, and try to put it into the match. All I can say is tomorrow is a day off for me and we're gonna think about the match tomorrow with my team."