Alcaraz holds off Evans to reach US Open fourth round
The top-seeded Spaniard breezed through his opening matches at Flushing Meadows and at first appeared on track for another easy win but had to find his best form after Evans mounted a third-set comeback.
He next plays Italian Matteo Arnaldi.
"He's a tricky opponent," Alcaraz said of Evans. "We made great points, great shots. A lot of different kinds of situations."
Alcaraz moved through the first set like a freight train, winning the first four games, and the 26th-seeded Evans failed to convert any of his three break points in the eighth game.
Evans did let out a roar as he broke Alcaraz with an unreturnable backhand down the line in the second game of the second set but the Spaniard broke back immediately and the Briton helped his opponent to another break in the fifth.
Alcaraz broke Evans again with a well-executed drop shot to close out the second set. However, Evans upped his level in the third set, channelling his frustration into a superb game seven where he broke with a backhand winner.
Alcaraz tapped into his superior speed and agility to tame Evans, 13 years his senior, in the fourth set, zipping back and forth along the baseline before breaking with a sublime forehand winner in the sixth game.
He finished the entertaining clash with another forehand winner, one of 27 in the match, prompting cheers of approval from the rapt crowd inside Arthur Ashe Stadium.
Across the plaza, 21-year-old Jack Draper offered British fans hope as he outlasted American wildcard Michael Mmoh 6-4, 6-2, 3-6, 6-3 to book his first trip to a Grand Slam fourth round.
He will face the winner of the clash between Russian eighth seed Andrey Rublev and France's Arthur Rinderknech.