Tiafoe, 24, is the youngest American man to reach this far at the US Open since 24-year-old Andy Roddick reached the final in 2006.
“It was definitely one hell of a show,” he said after the match. “I played really well today. Yeah, I guess, I mean, I just came out thinking I could do it. I helped him with that a few times.”
Earlier in the tournament, Tiafoe said he was happy to go mostly unnoticed.
After his victory on Monday, he expressed his delight at what his victory over Nadal meant to his parents, who immigrated to the United States from Sierra Leone.
“I’ve had a great passion for the game. Not even mainly for me, but to do it for them. To see them try me out beating Rafa Nadal, they saw I had big wins, but to beat these guys from Mount Rushmore, for them, I just can’t be I imagine what was going through their heads.
“Yeah, I mean, they will remember the day for the rest of their lives.”
Nadal, 36, scored his first major loss of the year and is now 22-1 this season. The Spaniard won the Australian Open and the British Open before withdrawing from Wimbledon in July ahead of his semi-final clash with Australian Nick Kyrgios.
“The difference is easy,” Nadal said afterwards. “You played a bad game and he played a good game. In the end that’s it, right?”
Nadal said Tiafoe played more aggressively than in the previous matches between the two, served well, had good backhands and was fast.
“But I don’t think I pushed him enough to raise the doubts I needed to create,” he said. “Of course, he did things well. If he wasn’t, he would undoubtedly not win. Congratulations to him.”
Nadal has said he needs to “fix things” and when he feels mentally ready to compete again he will, but is unsure of the schedule.
Tiafoe will face Russia’s Andrei Rublev in the quarter-finals on Wednesday.
The men’s singles final will be held at the US Open on Sunday.
Tiafoe’s parents met in the United States, where they had twins, Franklin and Francis.
Their father signed as a day laborer at the Junior Tennis Champions Center in 1999 in College Park.
While working on the clock, his father was forced to move into a vacant storage room at the tennis center, where his two boys slept with him, while their mother worked night shifts as a nurse. Tiafoe chose sports, played in the center for free, and fell in love with this sport.
Tiafoe previously said that while his family didn’t grow wealthy, he wouldn’t change anything.
He told reporters on Monday, “Being in tennis kind of made us go out of our way. My dad was able to watch us. It wasn’t supposed to be anything like that. Once we got into the tennis match, it was like my dad was like, It would be great if you guys could use this as a full scholarship to the school. I mean, we couldn’t afford the university.”
CNN’s Jill Martin contributed to this report.
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