It was an inspired serve-and-volley performance from Zverev, egged on by his younger brother Alexander Zverev, who pushed World No. 9 Rafael Nadal to five sets before losing on Saturday.
With the win, Zverev moves into his first Grand Slam quarter-final. He now plays the winner between No. 17 seed Roger Federer and fifth seed Kei Nishikori. Zverev has never played Nishikori, but has twice lost against Federer earlier, according to atpworldtour.com.
Competing in the fourth round of a Grand Slam for the first time, Zverev was unawed by his surroundings on Rod Laver Arena.
He rallied from 0-3 down in the first set by forcing Murray out of his game and even producing some vintage serve-and-volley moments, ultimately grabbing the opening set.
But Murray was not going to go away quietly. Although both players struggled on serve in the second set, with five of the 12 games highlighted by service breaks, the top seed was able to take control in most of the baseline rallies.
With Zverev serving at 5-6, Murray rifled a backhand winner on his first set point to level the match at one set each.
Zverev continued to put pressure on Murray with his return, breaking the top seed twice to take a commanding advantage in the match.
The German opened up the fourth set with an early break of serve and held his slight advantage the rest of the way.
Serving for the match at 5-4, a forehand error from Murray wrapped up the contest in three hours and 33 minutes.