Argentine 28th seed Del Potro defeated the 19-time Grand Slam champion 7-5, 3-6, 7-6 (10/8), 6-4 in Arthur Ashe Stadium, a court where Federer has dominated rivals from more than a decade.
"I think it's my home court too," Del Potro told the crowd. "You make me feel happy every time when I play here and I love your support."
Del Potro said he hopes to repeat his 2009 victory over Nadal ahead of his epic five-set victory over Federer to capture his only Grand Slam title.
"Against Rafa, hopefully I can repeat the result," Del Potro said. "I know against Rafa the crowd will be tough for me but I hope you are cheering for me again.
"He's number one in the world, but with this amazing support anything can happen."
Federer, who raced into the interview room after his defeat, praised Del Potro, saying, "Juan Martin fought like a lion."
"I feel like the way I'm playing right now it's not good enough to win this tournament. It's better I'm out and somebody else gets a chance to win."
The ruined possible first-ever New York matchup between Federer and Nadal, which had been a focus headed into the match, was an afterthought to Federer in the wake of a comprehensive loss.
"I didn't even think of it, that I lost so that match is not going to happen," Federer said. "I'm dealing with understanding what happened.
"Of course, it's a pity but Juan Martin deserves it more."
Federer made 41 unforced errors, nine more than his rival, and his 60 winners were 12 more than Del Potro, whose blistering serves took their toll.
"I served so good. I hit my forehands hard as I can. We play a great match and I deserve to win in the end," he said.
Del Potro, who has undergone four wrist surgeries since beating Federer eight years ago in the final, rescued four set points in the third set tie-breaker.
"I think I got lucky," Del Potro said. "I made a double fault in the 6-all and that cannot happen against Federer, but I got lucky. I made the good returns and in the fourth set I played even better.
"I cannot believe to play another semifinal after all my injuries."
Federer was at a loss to explain his loss.
"It happens. I don't know. It's hard to explain sometimes," Federer said.
"You do the right things and he does too and it matches up badly your way. I don't think I played badly. It didn't go my way."
As for the four squandered set points in the tie-breaker, Federer said, "I don't think those four points made all the difference. I missed too many balls.
"He came up with the goods and I helped him sometimes maybe."
Federer said in some ways he wasn't disappointed because he knew his game was weaker than it looked.
It has been a tough tournament. I struggled," Federer said. "If I ran into a good guy I knew I was going to lose. And going in I knew I'm not in a safe place.
"I'm out of this tournament because I wasn't good enough in my mind, my body and my game."