Tiafoe, 24, is the youngest American to reach that far at a US Open since then-24-year-old Andy Roddick reached the final in 2006.
“It was definitely a hell of a performance,” he said following the match. “I played really well today. Yeah, I think, I mean, I came out and I believed I could do it. That helps me play twice.”
Earlier in the tournament, Tiafoe said he was happy to go largely unnoticed.
After his win on Monday, he gushed about what the victory over Nadal meant to his parents, who immigrated to the United States from Sierra Leone.
“I had a lot of passion for the game. Not even mainly for me, but to do it for them. To see the experience of me beating Rafa Nadal, they’ve seen me win big, but to beat those Mount Rushmore guys, for them, I can only imagine what’s going through their heads. Couldn’t do it.
“Yes, I mean, they will remember today for the rest of their lives.”
Nadal, 36, recorded his first loss at a Grand Slam this year and is now 22-1 this season. The Spaniard won the Australian Open and French Open before pulling out of Wimbledon in July ahead of his scheduled semi-final clash with Australian Nick Kyrgios.
“The difference is easy,” Nadal said later. “I played a bad match, he played a good match. That’s it in the end, right?”
Nadal said Tiafoe played more solidly, served better, had a better backhand and was faster than in previous matches between the two.
“But I don’t think I pushed him enough to make him have the doubts I should have,” he said. “Of course, he did things well. If not, he wouldn’t have won, without a doubt, congratulations to him.”
Nadal said he “needs to fix things” and if he feels he is mentally ready to compete again, he will compete, but he is unsure of a timetable.
Tiafoe will face Russia’s Andrey Rublev in the quarter-finals on Wednesday.
The US Open men’s singles final is on Sunday.
Tiafoe’s parents met in America, where they had twins Franklin and Francis.
Their father signed up as a day laborer at the Junior Tennis Champions Center in College Park in 1999.
Working around the clock, his father was forced to move into an empty storage room at the tennis center, where his two boys stayed with him and slept there while their mother worked nights as a nurse. Tiafoe picked up the game, played free at center, and fell in love with the game.
Tiafoe previously said that while his family didn’t grow up rich, he wouldn’t change a thing.
He told reporters on Monday: “We’re kind of out of our neighborhood being around tennis. My dad’s watching us. There shouldn’t be anything like that. Once we got into the game. Tennis, it was like my dad, if you could use this as a full scholarship to school that would be awesome.” I mean, we couldn’t afford a university.”
CNN’s Jill Martin contributed to this report.