The Kiwis were all out for 183 after 45 overs. Australia replied with 186 for 3 in just 33.1 overs.
New Zealand's hopes of pulling off what would have been a famous win suffered a massive blow when skipper Brendon McCullum was bowled out by Mitchell Starc after just three minutes in the first over of the day.
The Kiwis recovered with a brilliant 83 from Grant Elliott and a slower 40 from Ross Taylor. But they then collapsed, with the loss of their last seven wickets for 33 runs to be all out for 183 in 45 overs.
Australia captain Michael Clarke, who made 74 off 72 balls, dedicated Sunday's victory to batsman Phillip Hughes, his close friend who died after being hit on the head by a bouncer last year in a first-class match.
Australia fast-bowling all-rounder James Faulkner was named man-of-the-match. The 24-year-old finished with figures of three for 36 from nine overs.
But it was his team-mate, fast bowler Mitchell Starc, who won the player of the tournament award. He reached a tally of 22 wickets during the competition.
Australia has won four of the last five World Cups - their only defeat going as far back as 1992.