New Zealand were boosted by a Shane Bond hat-trick and Ross Taylor's 84 before a late collapse when chasing the home side's 289 for eight at Bellerive Oval on Sunday.
The Kiwis were right in contention when Taylor and Peter Fulton (37) were together, before losing their last seven wickets for just 23 runs to finish on 184.
Wicketkeeper Adam Gilchrist took a fine diving catch to remove Taylor, who hit three sixes despite batting with a runner because of a sore groin, to end the 81-run partnership.
New batsman Craig McMillan was then run out for two by a direct hit from Michael Clarke at mid-on.
Man-of-the-match Andrew Symonds, who earlier hit 69 to boost Australia's total, took a spectacular two-grab catch high in the air to remove Fulton from Stuart Clark's bowling.
It was a disappointing end for the Black Caps, whose tight bowling had restricted Australia until Symonds and Cameron White (45) hit out in the closing overs.
Bond went for 22 in the 48th over before claiming New Zealand's second ever One-day international hat-trick in the final over.
The paceman removed White, Symonds and Nathan Bracken to emulate Danny Morrison's feat against India in 1994.
"I let myself down in the ninth over, but came back," he said.
Bond also dismissed Michael Clarke (33) to finish with 4-61, extending his amazing record against Australia which stands at 28 wickets in eight games at 12.35.
The Kiwis were able to rein in a flying start by the Australians, led by Gilchrist's 61, with rookie seamer Mark Gillespie taking 2-50.
Gillespie removed Matthew Hayden for 27 to end an 83-run opening stand and also claimed the prized wicket of Australian captain Ricky Ponting for 10.
Ponting has just 74 runs at 14.80 at his home ground in One-day internationals.
But Symonds batted with more caution than normal against some tight bowling before hitting out late on, reaching his 69 from 70 balls.
White survived two confident lbw appeals to make 45 from 32 balls, including three sixes, in a 90-run partnership with Symonds.
Australia rested Glenn McGrath and handed a debut to local fast bowler Ben Hilfenhaus, who impressed in taking 1-26.