The fourth seed was tested early on his serve, which was initially off target, but was able to maintain control of the contest with a strong returning display.
“There’s always things to improve, but I think I played a good match today,” said Zverev, who will face big-serving Canadian Milos Raonic in the fourth round.
After losing his serve once in the first set — and breaking three times — Zverev filled in any holes that could be exploited.
He picked up his first serve percentage to ease the pressure.
The German started to hold serve more comfortably and deftly handled the left-handed sliding serves delivered from the other end.
Bolt’s forehand constantly switched between being an asset and a liability.
The stylish left-handed swing was prone to both screaming winners and over-hitting which opened up break opportunities the German gladly accepted.
He said: “It’s sort of a blessing and a curse sometimes,” said Bolt. “I may have all this power, but sometimes the control isn’t always there.
“Sometimes what I struggle with is finding that balance between going for too much and not going for enough.”
Zverev promptly served out the match and muted his celebrations, aware that he had just outclassed a local favourite who had won over the crowd.
The result ended the uplifting run of the 26-year-old Australian who was digging ditches on building sites just three years ago during a career crisis of confidence.
Bolt entered the Australian Open without having previously won a match in a Grand Slam.
But he showed he belonged in the majors with two victories, which included a win over seasoned Frenchman Gilles Simon.