The Canadian reached his first grand slam quarter-final with a 6-4 7-6 (6) 3-6 3-6 6-4 in four gruelling hours.
Auger-Aliassime had only been the distance once before, losing from two sets ahead against Aslan Karatsev at last year’s US Open.
The 20-year-old also had a two-set lead against fourth seed Zverev, who has already played an incredible 25 five-set matches in his relatively short career, winning 16 of them.
Zverev looked a likely winner again when he finally rediscovered his first serve and levelled the match at 2-2.
But Auger-Aliassime found another gear just as Zverev’s serve deserted him in the decider.
“It’s a dream come true, unbelievable,” said Auger-Aliassime. “I’m just a normal guy from Montreal and here I am. Court One, Wimbledon.
“It’s surely the best victory of my life so far. With the roof closed the sound was crazy, like nothing I’ve experienced before.
“It was super difficult, I’ve never beaten Alex before, or even won a set against him. When he started serving better and things got difficult I had to dig deep.”