However, Grant Elliott and Ross Taylor rode New Zealand to 150/3 following the assault.
James Faulkner came into the attack and provided two quick breakthroughs.
He later dismissed the dangerous Elliott as well.
Faulkner finished with 36/3 as the Kiwis were bundled out on 183.
Lifting the trophy was surreal, says Faulkner
"Winning the World Cup was 10 times better than winning Player of the Match. When we received the trophy and Pup lifted it up on stage, it was unreal. The walk around the ground as well, seeing friends and family. It was surreal," Faulkner said.
Australia finished the chase with over 16 overs to spare
Australia lost Aaron Finch early on with Trent Boult dismissing him.
David Warner too departed in the 13th over, but contributed a pivotal 45 to set the tone for Australia.
Skipper Michael Clarke (74) and Smith (56*) then shared a 112-run stand for the third wicket to seal the game for Australia.
Faulkner was later rewarded for his match-winning performance in a high-voltage final.
Faulkner used his variations wisely in the final
Faulkner opened up on how he trapped Taylor and Elliott with his gutsy variations in the first innings.
"Taylor was starting to be a bit more aggressive, but it was just a gut feel to start with a slower ball," he said.
He added, "He threw the kitchen sink at it and that was the end of him. I gave him a little send-off."