The Spaniard retrieved a break in the third set but has been little troubled through his first two matches in New York after his opening-round tie was cut short by injury.
"I think I played a great match," said Alcaraz. "If I have to keep something from the match I'm going to keep the level from the second set."
"I had to forget that break (in the third set). I did such a bad game. I had to forget it and focus. To be able to win in straight sets is really important to me in the first rounds."
The 20-year-old, who will lose the number one ranking to Novak Djokovic after the tournament, plays Britain's 26th seed Dan Evans in the last 32.
Alcaraz is aiming to become the first man to defend the US Open crown since 2008, when Roger Federer hoisted the trophy for a fifth consecutive year.
