The first two sets brought a vintage performance on a sultry night from Nadal, who has dropped to world No 8 in what has been a lackluster season for the 29-year-old Spaniard.
Given his last chance to keep alive a 10-year streak of winning at least one grand slam title, 14-times major winner Nadal schooled the 18-year-old Coric over the first two sets.
But Coric responded with his best tennis and broke the Spaniard in the 10th game of the third set to send the match to a hard-fought fourth set.
The Spaniard finally prevailed thanks to a service break on a forehand service return winner in the seventh game.
"It's a very happy moment for me," said Nadal, returning to Flushing Meadows for the first time since his 2013 US Open triumph after missing last year with a wrist injury.
