Guillermo Vilas in 1977, is the only other of del Potro's countrymen to have won the US Open.
The 20-year-old sixth seed, beaten six times in previous meetings by Federer, denied the world number one a third grand slam of the year with a 3-6 7-6 (7/5) 4-6 7-6 (7/4) 6-2 victory at Arthur Ashe Stadium as the US Open stretched into a 15th day because of heavy rain that all but washed out play on Friday and much of Saturday.
The victory in four hours and six minutes saw Federer prevented from becoming the first man since American Bill Tilden in the 1920s to win the tournament six times in a row, and it was his serve that proved his major failing.
Federer could only manage a 54% first service rate and delivered 11 double-faults as del Potro clocked up 37 forehand winners, while the five-time champion converted only five of 22 break-points.
It also completed a grand slam season in which Federer, 28, had begun the year in tears as he lost the Australian Open final to Rafael Nadal but then won a first French Open title and broke Pete Sampras' record of all-time grand slam wins at Wimbledon with his 15th career title.
Both men had played wonderfully to win their semi-finals on Sunday, the champion defeating Novak Djokovic and del Potro demolishing Nadal. But this was 20-year-old del Potro's first grand slam final.
Any nerves the Argentinian might have had were not calmed by Federer's aggressive start to the match, breaking del Potro in his first service game and looking imperious at 3-0 up.
At 5-2, del Potro saved triple set-point on the way to a gutsy hold, provoking chants of 'Ole! Ole! Ole!' from his fans. Those were soon quietened, though, as Federer served himself into a one-set lead with an ace.
Federer remained on top at the start of the second as del Potro handed him his first break of serve with a double-fault before the Argentinian broke back to 5-5 with a wonderful forehand pass down the line - and then took the tie-break to level the match with a powerful forehand winner.
The third set was nip and tuck, del Potro breaking to 4-3 only for Federer to break back in the next game. Federer then went 5-4 up but was annoyed when del Potro was allowed to challenge after a long wait. The challenge failed, but Federer complained to chair umpire Jake Garner that the Argentinian had exceeded the time allowed to make the challenge.
"Don't you have any rules for this?" Federer asked Garner, whose response took the tension up a notch when he told the player to be quiet.
Federer was incensed and used expletives after saying to Garner: "Don't tell me to be quiet. If I want to speak I'll speak."
The anger was soon turned towards the del Potro serve, and the sixth seed double-faulted to give a set-point up to the Swiss.
To del Potro's dismay, he served another double-fault to gift the champion the set - and the Argentinian returned to his chair at the break and placed his head in his hands.
Federer served out the set, but del Potro rebounded from his setback by making the first break in the fourth set to go 3-2 up.
The Argentinian was beginning to enjoy himself, holding serve during a game in which he won a long rally with a forehand down the line and then 'high-fived' spectators along the side of the court.
Federer, by contrast, was all business - holding serve and then forcing a break point before del Potro netted one of his booming forehands and conceded his lead at 4-4.
A forceful hold of serve took Federer to the brink of victory, and del Potro did not start his service game in confident mood - falling behind 15-30 before producing a 128mph service winner and then a 131mph ace, holding serve with a rocket of a forehand winner down the line.
Federer looked to have responded in kind, opening with an ace and racing to 40-0 before saving two two break-points and recovering to win with an ace.
The set went to a tie-break, del Potro earning a mini-break at the start and taking the set when Federer sent a forehand return wide.
It was the first time Federer had been sent into a fifth set in a US Open final - and the decider did not start well for the champion, broken in the second game and falling 3-0 behind.
Del Potro moved to 5-2 by serving to love, clubbing another forehand winner off a backhand service return for the winning point.
Federer went 0-30 in the next game, and a wild backhand gave del Potro two championship points.
A nervous rally ended with the sixth seed scooping a forehand wide, and he netted a forehand return to deuce as Federer screamed 'Come on'. A much better forehand saved a game point for a second deuce, but Federer double-faulted again to bring up a third match point.
This time del Potro had his moment, Federer stretching in vain to send a backhand long as the 20-year-old fell to the ground to absorb the enormity of his victory.
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