Michael Clarke [ Images ] and Mike Hussey [ Images ] hit half-centuries in an unbroken, record partnership of 136 to help Australia amass 264 for five before New Zealand collapsed to 177 all out in the 42nd over.
Hamish Marshall was the only New Zealand batsman to show any real resistance, top-scoring with 55 from 87 balls. No one else made more than 27.
"It was a total we were confident of defending," Australia captain Ricky Ponting [ Images ] told reporters. "We were in a bit of trouble but Michael Clarke and Michael Hussey [ Images ] played beautifully."
New Zealand's chances of keeping the series alive were not helped by a horror start from opening bowler Daryl Tuffey [ Images ], later followed by an injury to opening batsman Michael Papps.
Tuffey conceded 16 runs off the first over of the match, which took 14 deliveries to complete after four no-balls and four wides.
Papps was then forced to retire hurt and taken to nearby hospital for precautionary checks after twice being struck on the helmet by Australia's express paceman Brett Lee [ Images ].
"We weren't good enough as we haven't been throughout the series," said New Zealand captain Stephen Fleming [ Images ]. "They never let us gain any momentum and we were outplayed in all departments."
Clarke, named man of the match, smashed an unbeaten 71 off 75 balls while Hussey made 65 not out from 73 deliveries as the pair set a one-day record for the sixth wicket for Australia.
Opener Simon Katich [ Images ], recalled for the injured Matthew Hayden [ Images ], gave the innings a flying start with 58 off 78 balls before the Kiwis struck back to reduce the world champions to 128 for five in the 29th over.
Left-arm spinner Daniel Vettori [ Images ] collected two wickets while Chris Cairns [ Images ] and Kyle Mills [ Images ] picked up one apiece to briefly put the brakes on the scoring before Clarke and Hussey's late charge.
Clarke struck six boundaries while Hussey hit three fours and a six as the pair bludgeoned 56 from the last five overs.
New Zealand were in immediate trouble when they lost Fleming for one and Nathan Astle for 27 after Papps had retired on three.
Marshall steadied the innings with his half-century but after he and his twin brother James, making his international debut, were run out by direct hits from Andrew Symonds [ Images ], New Zealand's victory hopes disappeared.
The teams play again in Wellington on Tuesday before the series finale in Napier [ Images ] next Saturday.
A.Gilchrist c Astle b Cairns 18
S.Katich lbw b Vettori 58
R.Ponting run out 11
D.Martyn lbw b Vettori 1
A.Symonds c Papps b Mills 21
M.Clarke not out 71
M.Hussey not out 65
Extras (lb-2 nb-10 w-7) 19
Total (for five wickets, 50 overs) 264
Fall of wickets: 1-68 2-85 3-90 4-117 5-128
Did not bat: B.Hogg, B.Lee, J.Gillespie, M.Kasprowicz
Bowling: Tuffey 2-0-25-0 (nb-5 w-4), Mills 9-0-57-1 (nb-4 w-1), Cairns 10-1-55-1 (w-2), Astle 9-0-47-0, Vettori 10-0-31-2 (nb-1), McMillan 10-0-47-0
S.Fleming b Lee 1
N.Astle c Gilchrist b Kasprowicz 27
M.Papps retired hurt 3
H.Marshall run out 55
C.McMillan c Hussey b Symonds 26
J.Marshall run out 14
C.Cairns c Hussey b Lee 12
B.McCullum c Hussey b Hogg 23
D.Vettori c Gilchrist b Hogg 0
K.Mills c Kasprowicz b Hogg 1
D.Tuffey not out 0
Extras (lb-8 nb-3 w-4) 15
Total (all out, 41.5 overs) 177
Fall of wickets: 1-7 2-45 3-114 4-135 5-136 6-161 7-162 8-171 9-177
Bowling: Lee 7-0-24-2 (nb-3 w-3), Gillespie 6-0-14-0 (w-1), Kasprowicz 8-1-28-1, Symonds 10-1-36-1, Hussey 3-0-22-0, Hogg 7.5-0-45-3
Result: Australia won by 87 runs
Man of the match: Michael Clarke (Australia)
First match: Australia won by 10 runs
Second match: Australia won by 106 runs
Fourth match: March 1, Wellington
Fifth match: March 5, Napier
Australia lead 3-0 in the series