New Zealand was favoured in their series-leading 100th cup final after beating Australia in the pool stage, and Fiji 22-19 in the semifinals.
But Australia struck first when Ben Dowling's break finished with Paterson cutting back off Matthew Gonzalez for the only try of the first half.
New Zealand hit back with converted tries by Akuila Rokolisoa from a stolen kickoff and Leroy Carter from Dylan Collier's offload.
Paterson tied the score on 14 with two minutes left with a second try in which he burned the New Zealand line with speed.
Then, after the fulltime hooter, New Zealand's Caleb Tangitau looked to be sprinting free on the outside but Paterson tackled him into touch, forcing extra time.
From Australia's kickoff, Josh Turner tapped the ball back to the Australians and it was spread wide for Paterson to run in and secure their eighth title in series history.
Paterson was asked which he liked most, the winning try or the try-saving tackle. He picked the tackle.