Alcaraz advances after Baez retires in U.S. Open first round
The pair were evenly matched in the first set with the 19-year-old Alcaraz getting the break in the last game, before hot and humid conditions tested both opponents in the second set.
Alcaraz, who became the youngest man to reach the quarter-final at Flushing Meadows a year ago, was not at his best as he produced 28 unforced errors in the 84-minute set, trading breaks with Baez twice before again getting the pivotal break in the final game.
Baez had a physio tend to his left leg before the third set but was unable to carry on, pulling up short and clutching his thigh as Alcaraz knocked a forehand winner across the net in the second game.
"I think both players and all of you don't deserve (an end) like this," Alcaraz told the crowd after the match. "Sebastian is a great player, he fights until the last ball."
The Roland-Garros quarter-finalist is among the favourites at the year's final major after picking up titles in Miami and Madrid, and was clearly appreciating his return to New York.
"I remember last year it was one of the best moments of my life," he said. "One year later, being four in the world is something special for me."