Tiafoe edged 22-year-old Michelsen 5-7, 3-6, 7-5, 6-3, 7-6 (10/6) to reach the semi-finals at Flushing Meadows for the third time in five years.
Tiafoe escapes Michelsen to reach US Open semi-finals
Frances Tiafoe rallied from two sets down and 3-0 down in the fifth set to hand Alex Michelsen a heartbreaking US Open defeat.
American 11th seed Tiafoe had all he could handle from his young compatriot, who hadn't dropped a set in reaching the first Grand Slam quarter-final of his career.
He was on the brink of another three-set win when he served for the match at 5-4 in the third, but a pair of double faults opened the door to Tiafoe and the more experienced player plowed through.
"I feel like I just handed it to him," a dejected Michelsen, ranked 46th in the world, said. "Then after that he started playing really good."
It would take two more sets before Tiafoe landed a forehand winner to clinch the 10-point match tiebreaker after four hours and 38 minutes, Michelsen weeping in the winner's arms as they met at the net.
"I was trying to keep it together, and I didn't do a good job of that," Michelsen said. "The match was very emotionally draining. Frances, he's such a good guy and he said a lot of personal things and just kind of got to me."
Michelsen had come out swinging on Arthur Ashe Stadium against an uncharacteristically passive Tiafoe, who usually feeds on the energy of the crowd.
"They were flat, but I was even more flat than the fans," Tiafoe said. "I was joking about that, but they definitely woke up as I started to pick it up."
After surviving the third set, he had a new lease of life, and even when Michelsen responded with an early break in the final set Tiafoe refused to fold.
"The moment is huge," said Tiafoe, who next faces either defending champion Carlos Alcaraz or eighth seeded American Ben Shelton.
"I've won a lot of great matches here. I've lost a lot of tough matches here as well. It feels amazing to get this done."
