Australia 181 (K D Mills 4-35) v New Zealand 182-8 (L R P L Taylor 64)
New Zealand beat Australia by 2 wkts
Daniel Vettori hit the final ball for four to give New Zealand a two-wicket success over Australia in the first one-day international.
Chasing a modest target of 182 under the Perth floodlights, Ross Taylor's 64 appeared to have set the Black Caps on course before a late stumble left five needed from the final over.
Skipper Vettori sealed his side's win in style, finding the point boundary with one required off Nathan Bracken's last delivery to give the tourists first blood in the five-match Chapell-Hadlee series.
Defeat for Australia also means they did not go back to the top of the International Cricket Council's one-day rankings after forfeiting their place at the top following the 4-1 series defeat to South Africa.
New Zealand's pursuit had started badly - Brendon McCullum (0) given out lbw to the second ball of the innings despite getting an inside edge on Shaun Tait's express inswinger.
Martin Guptill (13) was bowled by Bracken, and Peter Fulton (seven) well caught by Mitchell Johnson in his follow through to reduce the Kiwis to 25-3.
But Taylor took control of proceedings with a composed 97-ball knock, sharing solid stands with middle-order trio Grant Elliott, Neil Broom and Kyle Mills.
Elliott (eight) helped stabilise the innings during an alliance of 39 in 10.1 overs before he holed out to cover off medium pacer James Hopes (1-23), while Broom had contributed 29 to a 42-run stand when controversially dismissed.
He departed after appearing to be bowled by Michael Clarke's left-arm spin (1-18), but replays showed wicketkeeper Brad Haddin had removed the bails with his gloves while taking the ball in front of the stumps.
However, Mills added 67 with Taylor, including the use of the batting powerplay from overs 43-47, to take New Zealand to the brink of victory.
Both fell with the finish line in sight, Mills (26) cleaned up by a Tait (2-40) yorker and Taylor caught at backward point off Bracken to leave 12 still needed off the final 15 balls.
The equation came down to five required from the final over, bowled by Bracken (3-35).
Despite Tim Southee (3) being bowled by the second delivery, Vettori was on strike for the final ball with one needed and - with the field up - duly found the boundary to seal the win.
Australia had earlier posted a below-par total of 181, Michael Hussey's 49 the only highlight.
Mills did the initial damage, removing inexperienced opening pair Shaun Marsh (15) and David Warner (7) during his opening spell.
The untimely run outs of Ponting (5) and Clarke (12) reduced the hosts to 51-4 in the 18th over and it soon became a full-blown crisis at 54-5 when David Hussey (13) was caught behind down the leg side off the bowling of off-spinner Jeetan Patel (1-47).
Michael Hussey and Haddin stemmed the tide with a 61-run stand for the sixth wicket, but those runs came at a laboured pace - mainly due to the stifling left-arm spin of Vettori, who conceded just 22 from his 10 overs.
Eventually Haddin's patience broke and he played on to his own stumps after advancing down the wicket to Mills for 31 from 54 balls.
That left Australia 115-6 from 35 overs and while Michael Hussey (49) and Hopes (18) put on 27 to set the scene for a late attack, both fell in the first over of the Australians' batting powerplay, bowled by Iain O'Brien (2-43).
Michael Hussey chipped tamely to mid-off and Hopes followed three balls later, caught in the same position from a miscued attempt to clear the off-side.
Bracken was then trapped lbw for a duck by Southee (1-34) in the next over.
Johnson and Tait (nine not out) frustrated the visitors briefly in their 27-run stand for the last wicket, but Mills had the final say when he bowled Johnson (20) with the fourth delivery of the penultimate over to finish with 4-35.
The second instalment of the series takes place in Melbourne on Friday.