The 20-year-old Argentine, who stayed alive by winning two tiebreaks, gained confidence as he moved through his first career grand slam and charged to victory, breaking Federer in the last game to end their four-hour, six-minute struggle.
The 6-foot-6 (1.98 m) Del Potro lay down on his back and covered his tear-streaked face with his hands after the 28-year-old Swiss sailed a backhand long on the Argentine's third championship point.
"I had two dreams this week," the sixth-seeded Del Potro said at the trophy presentation.
"One was to win the US Open and the other one is to be like Roger. One is done, but I need to improve a lot to be like you," he said, looking at Federer, winner of a record 15 major titles.
"You fought until the final point. You are a great champion.
"I'm very happy to be here with this crown, with these people, on this court ... This will be in my mind forever."
Del Potro became the second Argentine to win the US men's crown, joining compatriot Guillermo Vilas, who won on clay in 1977, and was watching the final at Arthur Ashe Stadium.
The Argentine had never beaten Federer in six previous meetings, losing to the Swiss master in the semi-finals of the French Open after taking a two sets to one lead.
EARLY JITTERS
Del Potro overcame some early jitters and a first set that saw him struggle with his first serves and heavy forehand in breezy conditions at the National Tennis Center.
But as the match wore on, the young Argentine began to find the range and fire away.
Del Potro won the second-set tiebreaker 7-5, and after double-faulting the last two points to lose the third set, battled the world number one to another tiebreaker.
The Argentine won that decider by 7-4 to set up the first Open five-set final since Andre Agassi topped fellow-American Todd Martin 10 years ago.
Taking advantage of Federer's faulty serve, Del Potro broke the French Open and Wimbledon champion in the second game of the fifth set and cemented his advantage by breaking the Swiss master again in the final game.
"I got off to a good start and had many more chances to make a difference," Federer told reporters. "He hung in there and gave himself chances, and in the end he was a better man."
Del Potro had 37 winners off his huge forehand and took advantage of a poor serving performance by Federer, who successfully landed only half of his first serves and double-faulted 11 times.
Federer, whose last defeat at Flushing Meadows came against Argentine David Nalbandian in the fourth round of the 2003 tournament, fell short of matching American Bill Tilden's mark of six U.S. titles in a row in the 1920s.
"You can't have them all," he said.
"I've had an amazing summer and a great run."
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