Tiafoe is aiming to snap a 21-year US drought in the men's majors but he had to dig deep to hold off the hard-hitting Popyrin, feeding off the energy of the home crowd at Arthur Ashe Stadium where he dreamed of playing as a child.
Australian Popyrin was fresh off the biggest win of his career after beating defending champion Djokovic in the third round and while he fired down 24 aces he also coughed up nine double faults and had some costly unforced errors.
Tiafoe thanked the fans at Arthur Ashe for their support.
"(This court) brings out the best in me and you guys are unbelievable fans," he said.
"Without you guys, it wouldn't have happened."
He added: "Seeing the Williams sisters win titles here, seeing Roger (Federer) win here a million times, I was like, I want to play on this court and it's so iconic - obviously named after Arthur Ashe," said Tiafoe, who next plays ninth seed Grigor Dimitrov.
"I wanted to be part of that and it brings out the best in me."
The men's draw has already lost some of its biggest names with Djokovic and third seed Carlos Alcaraz out early and only one former champion remaining in the men's draw, but Tiafoe is not getting ahead of himself.
"I'm just day by day, literally," said Tiafoe, who stunned Rafa Nadal two years ago en route to his first major semi-final.
"Grand Slams, two weeks, a lot going on. You can't get ahead of yourself and look at what could happen and things shaking out. Everyone is good, so it doesn't really matter who's in or who's not."
Tiafoe fended off two break points in the fourth game and broke the Australian from the baseline in the ninth in a superb opening set.
Popyrin built up momentum early in the second set, holding his serve in a five-deuce third game before converting on break point with a perfectly placed drop shot in the fourth.
But after the Australian handed Tiafoe a break with a double fault the American sprinted through the tiebreak with a red-hot forehand.
Popyrin broke to love in the third game of the third set and got a two-break lead with a backhand winner in the seventh before closing out the frame.
The Australian, who won the Canadian Open last month, then ran out of steam and handed Tiafoe a break with a double fault in the sixth game of the final set.
Tiafoe clinched it on the third match point with a forehand winner that just kissed the line and he flexed his muscles to the cheering home crowd in celebration.
Tiafoe next plays Bulgarian ninth seed Grigor Dimitrov in the quarter-finals.