The big-serving fourth seed blasted 15 aces on Wednesday (Thursday AEST) and employed drop-shot finesse at the net to preserve his hopes of capturing his first major after finishing runner-up at Roland Garros.
Zverev proved too much for the world No.77. Muller committed 41 unforced errors and battled through an apparent leg injury in brutal temperatures and high humidity at Flushing Meadows.
The beaten men's finalist in New York in 2020, Zverev came out firing, breaking Muller's serve in the first game before ultimately claiming the back-and-forth first set.
Clutching his upper right leg, Muller left the court for a lengthy medical time-out between sets but returned with a vengeance.
The resilient Frenchman stood two points from taking the second set, but the world No.4 fought back to take the final five points of a tiebreaker.
Zverev cruised through the third set, closing out the match with a final ace.
The German  will next face Argentina's Tomas Etcheverry, who beat fellow countryman Francisco Cerundolo 6-3 4-6 6-4 1-6 6-3.
In other second-round action, big-hitting Frances Tiafoe did his bit to boost American hopes. Tiafoe was leading 6-4 6-1 1-0 when Kazakhstan's Alexander Shevchenko retired.
American Frances Tiafoe has progressed to the third round of his home grand slam. (AP PHOTO)
"Happy to get it done. Hate to win it that way but overall I thought I actually played pretty well today," said Tiafoe, who reached the New York semi-finals in 2022.
It may have been a stress-free victory but Tiafoe still changed shirts five times in the hot, humid conditions.
Tiafore's third-round opponent is another American, 13th-seeded Ben Shelton, who beat Spain's Roberto Bautista Agut 6-3 6-4 6-4.
The all-American encounter is a rematch of last year's quarter-final, which Shelton won in four sets.
Jiri Lehecka of the Czech Republic came back from two sets down to survive a stern test against American qualifier Mitchell Krueger 6-7 (5-7) 0-6 6-4 6-4 7-5.
Russian sixth seed Andrey Rublev also produced a superb comeback from two sets down to defeat Frenchman Arthur Rinderknech 4-6 5-7 6-1 6-2 6-2.
Italian 18th seed Lorenzo Musetti also overcame a wobbly start to beat Serbian Miomir Kecmanovic 3-6 6-4 6-4 2-6 7-5 in three hours and 47 minutes.
One of the biggest surprises of the day came when unseeded Argentinian Francisco Comesana recovered from a set down to upset 17th-seeded Frenchman Ugo Humbert 5-7 6-4 6-4 6-4.
Dutchman Tallon Griekspoor reached the third round for the first time after 21st seed Sebastian Baez of Argentina withdrew from their match in the second set.
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