A maiden going into the weight-for-age race, the Danny O'Brien-trained Shamus Award staved off a desperate lunge from Happy Trails to score by a half head.
Fiorente was a long neck away third with Foreteller finishing fourth.
One of the outsiders, Shamus Award's victory gave champion apprentice jockey Chad Schofield his first Group One success.
Shamus Award held the inside running to the first turn and maintained a solid gallop.
He edged away from Fiorente turning into the straight and looked set for a clear-cut victory until Happy Trails unwound with his finish.
Shamus Award only made it into the Cox Plate field when the headline mare Atlantic Jewel was scratched.
It was the only piece of fortune the colt needed, according to O'Brien.
"Today we just got our chance to get out there and make our own luck and show what a good colt this is," O'Brien said.
"He could of easily been a Guineas winner and a Cox Plate winner, but we're pretty happy to take the Cox Plate."
New Zealand star It's A Dundeel finished unplaced after being trapped wide for most of the race.