Del Potro cruised through most of his match against countryman Diego Junqueira and served for the contest at 5-4 in the third set, but the 2009 champion played a poor game to lose serve and then appeared weary during a long ensuing game on his opponent's serve.
He eventually broke, however, for a 6-5 lead and then served out the match on his second try for a 6-2, 6-1, 7-5 win.
The second-ranked Nadal, meanwhile, faced little resistance against Nicolas Mahut, breaking his opponent twice in each of the first two sets before the Frenchman retired down 6-2, 6-2.
Nalbandian has defeated the 25-year-old Nadal twice in four career meetings, although both of those wins came in 2007 when Nalbandian finished the year in the top 10.
Now 29, his ranking currently stands at 76.
Del Potro in 2009 became the second Argentine men's player (Guillermo Vilas) to win the U.S. Open, defeating the two greatest players of the past decade - Nadal and Switzerland's Roger Federer - in the semifinals and final, respectively, to capture the title.
He also was the first Argentine to win the tournament on its current hard-court surface, but he was unable to attempt a title defense in 2010 because he had not yet fully recovered after undergoing wrist surgery earlier that year.
Del Potro's ranking fell to as low as 485, but he has quickly climbed back into the top 20 with several strong results in 2011.
The U.S. Open is the last of the four Grand Slam events on the tennis calendar.