New Zealand had to win the third and final game to retain the trophy, but could not maintain a strong start to the match.
They were dismissed for 168 from 34 overs in reply to Australia's 6-282 from 50 overs and lost the series 2-0.
Australian captain Ricky Ponting was named man of the match and man of the series.
He scored a superb unbeaten 134 from 133 balls after 107no in game one, while game two was washed out.
The only New Zealand batsmen to offer genuine resistance were No.4 Scott Styris and tailender Mark Gillespie.
Their ninth-wicket stand of 40 from 28 balls was the best of the innings.
Brett Lee, who took 3-47, bowled Styris for 75 and Brad Hogg also snared his third wicket when he had Gillespie caught at mid-wicket for 24 to end the match.
But Hogg had an average bowling return as he tries to force his way into the Boxing Day Test side.
His six overs returned 3-49, but included some punishment from No.10 Gillespie, who was batting with a runner.
Earlier, New Zealand all-rounder Jacob Oram conceded only five runs from his first five overs to give Australia early trouble.
His opening spell over eight overs returned 2-18 and he finished with 2-34 from 10.
Australia were in trouble at 3-87 in the 20th over, but that brought together Ponting and Andrew Symonds.
They put on 114 for the fourth wicket to first steady the innings and then effectively take the match away from New Zealand.
Symonds made 52 before Kyle Mills trapped him lbw, one ball after reaching his half-century with a boundary.
Ponting gave a half-chance on 25 when a shot off his toes landed just short of mid-wicket, but otherwise he was in top form.
His innings featured 10 fours and two sixes.
The skipper's previous best one-day international score at his home ground was only 37.