The big-serving fourth seed blasted 15 aces and employed a drop-shot finesse at the net to preserve his hopes of capturing a career-first major after a runner-up finish at Roland Garros.
Zverev proved too much for world number 77 Muller, who committed 41 unforced errors and battled through an apparent leg injury in brutal temperatures and high humidity at Flushing Meadows.
The German came out firing after a shaky round-one performance, 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 timeout between sets but returned with a vengeance.
The resilient Frenchman stood two points from taking the second set but the world number four fought back to take the final five points of a tiebreak, blasting a line-hugging forehand for the winner.
Zverev cruised through the third set, closing out the match with a final ace.
