After cruising through the opening set and surrendering the next, Zverev gained a foothold in the see-sawing third set when he grabbed a 4-2 lead but a sudden spell of rain halted play on John Cain Arena and threatened to disrupt the German's rhythm.
With the roof closed and court towelled dry during a near 40-minute break, the third seed got back to work and barely skipped a beat on serve as he comfortably closed out the set to regain control of the contest.
Zverev broke Muller for a sixth time early in the next set but the three-time Grand Slam runner-up paused at 2-1 and sat down in his chair with what appeared to be a leg problem before the 28-year-old soldiered on after medical treatment.
Some big winners followed from Zverev's racket as he looked to shorten his time on court, and he squandered two match points before delivering the knockout blow in the form of a big ace to book a meeting with British 26th seed Cameron Norrie.