Australia's fast bowlers, with Mitchell Johnson taking four wickets, led the way as New Zealand were bowled out for just 206 with nearly five overs of their innings left.
Left-armer Johnson finished with four for 33 and Shaun Tait three for 35.
That New Zealand even had the remotest chance was down to a battling fifty from Nathan McCullum and skipper Daniel Vettori's 44 with the duo combining well in an eighth-wicket stand of 54.
The Black Caps had earlier been in dire straits after their top order collapsed to 73 for six against the quicks from 66 for two.
Australia finished on 207 for three with a mammoth 16 overs to spare with Michael Clarke (24) and Cameron White (22) the not out batsmen as Australia also won the Chappell-Hadlee Trophy. Opener Shane Watson top-scored with 62.
"It was a good game for us. New Zealand are a very good one-day side, a very competitive team and for us to win as well as we have today is pretty satisfying," said Australia captain Ricky Ponting.
"Things worked out well. The fact that we got early wickets meant that I could keep attacking with the quick bowlers."
Vettori admitted his team had suffered a disappointing performance.
"We got off to not a bad start but losing three or four wickets in that clump really hurt us. We were fortunate that Nathan McCullum (52) played the innings he did to give us a chance," he said.
"We are going to have to move past this result pretty quickly. We've got Zimbabwe in about seven or eight days so maybe a good break is a good thing for us. We can get our heads around a must-win game."
Australia openers Watson and Brad Haddin were rarely troubled during a century first-wicket stand.
Haddin, a fluent strokemaker, brought up his fifty in 39 balls with eight fours while Watson went to the landmark in 52 balls including a six off a Nathan McCullum off-break.
New Zealand's day appeared to be summed up when substitute Kane Williamson, at deep mid-wicket, dropped Watson on 59 off left-arm spinner Vettori.
But the Black Caps gave themselves a glimmer of hope when 133 without loss became 136 for two when fast bowler Hamish Bennett removed both openers in the space of three balls in the 19th over.
Haddin (55) hooked a looping bouncer to James Franklin and then Watson (62) inside-edged an intended square-cut onto his stumps.
Ponting meanwhile could only manage 12 before he was brilliantly stumped down the legside by Brendon McCullum off Southee.
In a match played out against the backdrop of the Christchurch earthquake, Ponting won the toss and chose to field in overcast conditions.
Tait, following the economical Brett Lee, removed dangerman Brendon McCullum for 16 when an attempted carve over the covers flew straight to Jason Krejza at third man.
Jesse Ryder hit six forceful fours but Johnson took two wickets in four balls in the 14th over to have the left-hander and Franklin edging to wicketkeeper Haddin as they both pushed limply at good length deliveries.
Tait then had Scott Styris caught behind for a duck and yorked Ross Taylor, who struggled to make seven off 22 balls.
One concern for Australia coming out of this match though would have been the way Nathan McCullum milked rival spinners Krejza and Steven Smith -- whose combined 18 overs yielded just one wicket for 91 runs.
Nathan McCullum top-scored for the Kiwis, completing a 72-ball fifty including three boundaries before he was lbw to Johnson for 52.
M Guptill b Watson 10
B McCullum c Krejza b Tait 16
J Ryder c Haddin b Johnson 25
R Taylor b Tait 7
J Franklin c Haddin b Johnson 0
S Styris c Haddin b Tait 0
J How lbw b Smith 22
N McCullum lbw b Johnson 52
D Vettori c Haddin b Lee 44
T Southee c Ponting b Johnson 6
H Bennett not out 0
Extras (b1, lb8, w13, nb2) 24
Total (all out, 45.1 overs) 206
Fall of wickets: 1-20 (B McCullum), 2-40 (Guptill), 3-66 (Ryder), 4-66 (Franklin), 5-67 (Styris), 6-73 (Taylor), 7-121 (How), 8-175 (N McCullum), 9-206 (Vettori), 10-206 (Southee)
Bowling: Lee 8-2-29-1; Tait 7-0-35-3 (2nb, 4w); Johnson 9.1-3-33-4 (2w); Watson 3-1-9-1 (1w); Krejza 9-0-47-0 (1w); Smith 9-0-44-1
S Watson b Bennett 62
B Haddin c Franklin b Bennett 55
R Ponting st B McCullum b Southee 12
M Clarke not out 24
C White not out 22
Extras (lb3, w29) 32
Total (3 wkts, 34 overs) 207
Did not bat: D Hussey, S Smith, M Johnson, B Lee, S Tait, J Krejza
Fall of wickets: 1-133 (Haddin), 2-136 (Watson), 3-167 (Ponting)
Bowling: Southee 10-2-45-1 (4w); Vettori 7-0-39-0 (1w); Bennett 7-0-63-2 (7w); N McCullum 3-0-22-0; Ryder 5-0-24-0 (3w); Franklin 2-0-11-0
Result: Australia won by seven wickets