The 21 year-old cruised to a 6-3 6-3 6-2 third-round victory over Bolt in only one hour and 52 minutes, meaning he joined a frustrated Novak Djokovic in the last 16.
World number one Djokovic needed four sets to beat Denis Shapovalov, the 25th seed, prevailing 6-3 6-4 4-6 6-0 despite having a meltdown in the third after disagreeing over when the floodlights were switched on at Rod Laver Arena.
Number 12 seed Fabio Fognini was the biggest casualty on Saturday, the Italian going down in four sets to Pablo Carreno Busta, while David Goffin was another seed to fall as he lost in straight sets to Daniil Medvedev.
Kei Nishikori, Milos Raonic, Borna Coric and Lucas Pouille all won their third-round matches.
'ASPARAGUS' ZVEREV LIGHTS UP DAY SIX
Zverev made light work of Bolt, setting the tone by breaking serve in the first game of the match.
The German was only broken once in the match and hit 29 winners en route to booking a meeting with Raonic, the first time he has reached round four in Melbourne. It ended an impressive run from Bolt, ranked 155.
After the match, Zverev produced further entertainment for the crowd when asked about the impact of fitness trainer Jez Green, who formerly helped Andy Murray to bulk up.
"I'm still the skinny dude on tour!" Zverev said. "When [Green] started working with Andy, you can actually see he became one of the strongest dudes on tour.
"Whereas I’m still looking like - I don't know - I have been called asparagus or something a few times!"
DJOKOVIC UNHAPPY BEFORE PROGRESSING
Djokovic will meet Medvedev next, though he dropped a set for the first time in the tournament against Canadian teenager Shapovalov.
The top seed was 4-1 up in the third before being broken twice to lose the set, and received a code violation for swearing as he criticised the decision to turn the lights on while the sun was still shining. He recovered his focus to win the fourth set 6-0, but overall he had 16 winners to 33 unforced errors.
"The lights being switched on at 5pm was completely unnecessary and I was agitated," he said after the match, revealing the request had come from TV broadcasters.
"It should not happen to me. I should know better. I have experience but it does happen. I allowed him to come back to the match but I like the fact I was tested."
MEDVEDEV: DJOKOVIC NOT WHAT HE WAS
Rising star Medvedev reached the last 16 of a grand slam for the first time by beating Goffin 6-2 7-6 (7-3) 6-3 with 31 winners, and wasted no time talking up his chances of upsetting Djokovic.
"What I can only say is that probably he is not playing as he was before," the 15th seed told reporters of his upcoming opponent.
"Or that's just [my] feeling. Because before, when he was young, I was just watching on TV but it was just something insane when he was playing Andy or somebody for five hours and you couldn't see one down [level], it was only up.
"It's not the same right now, you always have chances to beat him. That's why he lost three times to 'Next Gen' players last year and I'm going to try to find my chances."
AUSTRALIAN INTEREST ENDS DESPITE POPYRIN HEROICS
There will be no Australian players in the second week after wildcard Alexei Popyrin joined Alex de Minaur and Bolt in losing in the third round, despite putting up a brave and impressive fight to battle back from two sets down against Pouille.
In front of a vocal home support in the last match of the day, the 19 year-old ultimately fell in five sets to the number 28, the match finishing 7-6 (7-3) 6-3 6-7 (10-12) 4-6 6-3 after three hours and 43 minutes.