The Spanish world number one became the second man in the Open era, behind Andre Agassi, to reach the last four at Flushing Meadows three times before turning 21.
Alcaraz, looking to do the Wimbledon and US Open double, will face Russian third seed Daniil Medvedev in Friday night’s semis and remains on course for another final showdown with Novak Djokovic, who he beat in July’s epic SW19 showpiece.
Zverev, the German 12th seed, has proved he is back at the top of the sport this fortnight after eight months out following the horror ankle injury he suffered against Rafael Nadal at last year’s French Open.
But the 2020 runner-up was unable to halt the Alcaraz juggernaut in a 6-3 6-2 6-4 defeat inside Arthur Ashe Stadium.
The first set was evenly poised on serve at 3-3 when Alcaraz, by no means at his electric best, took control of the match.
He won six of the next seven games to go a set and a break up, and Zverev needed a medical time-out after Alcaraz, clapping sawdust onto his hands to get a better grip of his racket on a horribly humid night, moved two sets ahead.
Zverev forced two break points at 2-2 in the third, but when they disappeared his chances went with them as Alcaraz broke for 5-4 and served out for the victory in two hours and 29 minutes.
“To see him in the quarter-finals of a grand slam playing at his best, I’m so happy,” said Alcaraz of his opponent.
“We enjoy his game and we are really happy to have him back.”
The 20-year-old added: “I’m feeling comfortable playing in this court, playing in New York.
“I’m showing my best level. I’m feeling good physically and ready for a good battle in the semi-final.”