Coric defeated Nadal 7-6 (11/9), 4-6, 6-3 in the 36-year-old Spaniard's first match since suffering an abdominal injury in a Wimbledon quarter-final victory and withdrawing before the semi-finals.
With the loss, 22-time Grand Slam winner Nadal cannot overtake top-ranked Daniil Medvedev for the world number one spot and a top seeding at the US Open.