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The Spaniard struggled to handle Del Potro's serve and huge forehand in the opening set before finding his stride to set up a title-decider with South Africa's Kevin Anderson on Sunday.
Del Potro, who had played a total of nine sets in the two previous rounds as Nadal cruised into the last four, ran out of gas and looked toothless against the Spanish juggernaut.
Nadal ended the 2009 champion's ordeal with a splendid backhand passing shot on his first match point, four years after his last title at Flushing Meadows.
"It's been an amazing season for me and I'm so happy to get a chance to fight for another title after a couple of seasons with injury troubles," said Nadal, who won a record-extending 10th French Open title in June.
"It means a lot to me. I had to change a couple of things after the first set because I was playing on his backhand too much and he was waiting for me there.
"So I tried to move him around more and be more unpredictable. I was not playing bad in the first set but I lost it so some things had to change."
Del Potro was dominant early, hammering Nadal with his forehand and serving strongly to put the Spaniard in full-defence mode.
The Argentine closed out the first set with a lightning quick forehand.
Nadal's response was devastating, breaking Del Potro three times in succession and conceding only one unforced error to dole out a bagel in the second set.
The Spaniard maintained the pressure, a forehand winner down the line capturing an early break and a 2-0 lead in third set.
Having lost nine consecutive games, Del Potro finally held serve to trail 3-1 and started hitting big forehands again.
But Nadal stayed in control and sealed the set with a fine overhead.
"Rafa just play even better the last three sets of the match, and I couldn't hit my backhand as good as I did in the beginning of the match," said Del Potro.
"He played so smart from the second set till the end of the match.
"To be honest, I'm angry to lose a chance like this but maybe tomorrow I will be calm and see how big the tournament was for me."
An exhausted Del Potro began netting easy shots and found himself down an early break in the fourth set.
The 31-year-old Nadal, with his teeth firmly in his prey, showcased his defensive class to turn things around on match point and set up a strong chance for more grand slam silverware.