Norrie was again well-backed at Melbourne Park, having enjoyed some of the best crowd support of his career during his second round win over American Emilio Nava.
The 26th seed had been a break up in the first set but, after losing it, launched a positive response.
A Zverev swipe into the net at 5-4 down in the second set allowed Norrie to convert his first break point since the second game of the match and level things up.
But the Briton, yet to defeat a top-five ranked player at a Grand Slam, had his momentum halted just three games into the third set – and Zverev made certain with a second break to regain his advantage.
Norrie was left shaking his head as he watched the fourth set quickly unravel, with Zverev powering to an efficient conclusion.
A 16th ace after two hours and 46 minutes polished off a third consecutive four-set win for Zverev at Melbourne Park, where his pursuit of a maiden Grand Slam title will continue against Argentine Francisco Cerundolo.
“It will be interesting to see what route Norrie goes over the next few months,” British coach Dan Kiernan told BBC Radio 5 Live Sports Extra.
“His level has been there but he doesn’t have that consistent firepower to be beating Zverev regularly on the big show.
“It would take a bit of a change in identity.”