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Chasing a revised target of 200 runs off 34 overs - which definitely favoured the home team - as rain delayed the start of their innings, Australia lost Brad Haddin for a duck in the first over to a fired-up Shane Bond.
Ricky Ponting (50 off 35 deliveries) and Shane Watson (32), however, countered a feisty Bond and as soon as he was rested after his first spell, laid into Daryl Tuffey and Tim Southee - taking 39 runs in three overs off these two.
Daniel Vettori restored some sanity with his trademark guile, picking up Watson, and two overs later, Ponting, for his trouble.
Cameron White continued with his amazing summer, and together with Adam Voges were content to nudge the ball around, only collecting the odd boundary and keeping the team on track for victory.
The pair added 65 for the fourth wicket and when Voges departed for 34, Michael Hussey was in no mood to be trifled with and hit a quick 17-ball 28 to safely see the visitors through with 17 balls remaining.
Man-of-the-Match, White, finished unbeaten on 50.
Earlier, Australia dismissed New Zealand for 238, having asked the hosts to bat first for the second time in consecutive matches.
Nathan Hauritz was the pick of the visitors' attack, as New Zealand folded from 120/1 to a below-par 238 all out inside 45 overs.
Some soft dismissals, combined with telling pressure, were their downfall - none more so than the loss of Brendon McCullum for 61, just when he was looking to accelerate through the middle of the innings.
McCullum and Ross Taylor threatened Australia with a 57-run stand, but Taylor wasn't quite as fluent and on 15 targeted the short square-boundary with a flick off James Hopes only to be well caught by Michael Hussey running around from deep midwicket.
That piece of class fielding sparked Australia and they collected five wickets in 11 overs as the middle order struggled, failing to strike a boundary for 22 overs.
Hauritz finished with 3/46, and his only blip came when Daryl Tuffey lifted him over the boundary for three consecutive sixes, over square leg, midwicket and straight down the ground, in an over that cost 22.
Tuffey, who in 87 previous ODIs had only hit one six, also cleared the boundary off Watson and finished with his highest one-day international score of 34.
Shane Watson, James Hopes and Mitchell Johnson bagged two wickets each.
The final ODI is in Wellington on Saturday, March 13.
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