The American 12th seed had lost all four of his previous matches at this stage of a major but edged out 2020 runner-up Zverev 7-6 (7-2) 3-6 6-4 7-6 (7-3).
He roared in delight as Germany’s Zverev pulled the final ball wide before holding his arms aloft to take the acclaim of the crowd on Arthur Ashe Stadium.
The win keeps alive Fritz’s bid to become the first American men’s singles champion at Flushing Meadows since Andy Roddick in 2003.
“Today just felt different,” Fritz, 26, said.
“I really felt like it was my time to go a step further. It’s only fitting I’m doing it here on this court, at the Open, in front of this crowd.”
Fritz could play another American in Frances Tiafoe for a place in a first Grand Slam final.
Tiafoe meets Bulgarian Grigor Dimitrov in the quarter-finals during Tuesday’s night session.
Fritz’s victory followed New Yorker Emma Navarro beating Paula Badosa to reach the semi-finals of the women’s singles.