Djokovic snuffed out Fritz's hopes of becoming the first American man to win a Grand Slam singles title since 2003 with an impressive quarter-final victory on the Arthur Ashe Stadium court.
The win sent the 38-year-old Serbian - chasing a record-breaking 25th Grand Slam victory - into a mouthwatering semi-final against Spanish second seed Alcaraz on Friday.
Djokovic clinched victory when fourth seed Fritz double-faulted on match point in the 10th game of the final set and could not hide his relief at finally emerging victorious.
"In this kind of match a few points on either side decide the winner," he said. "It was an incredibly close match. It was really anybody's match."
Fritz was left ruing his failure to make the most of the opportunities that came his way, converting only two of 13 points during an absorbing three-hour 24-minute battle.
The American fourth seed squandered five break points in the opening set that would have made it 5-4, instead allowing Djokovic to wriggle off the hook and take a one-set lead.
Then, after battling back to break Djokovic to get to 5-5 in the second, Fritz was broken immediately to surrender the initiative.
Djokovic duly held to take a two-set lead, and while Fritz hit back to take the third set, the veteran Serb regrouped to wrap up victory in the next set.
"I thought I was really lucky to save some crucial break points in the second set," Djokovic said. "I think for most of the second and third sets he was the better player."
Djokovic will meet Alcaraz in the last four with the 22-year-old Spaniard in blistering form.
