Australia's misery continued, with New Zealand beating them by two wickets in Perth on Sunday in a low-scoring first ODI in the five-match ODI series.
Chasing a victory target of 182, New Zealand huffed and puffed before Ross Taylor (64) propped them.
Needing five runs off the last over, the Kiwis levelled the score with the fifth ball before captain Daniel Vettori hit a boundary off the last delivery from Nathan Bracken for a memorable win.
Earlier, after Australia captain Ricky Ponting decided to bat first, Kiwi spearhead Kyle Mills (4/35) and his bowling colleagues skittled out the hosts for 181 in 48.4 overs.
The score could have been even more embarrassing for the hosts but for some useful contributions from Michael Hussey (49) and Brad Haddin (31).
Like Australia, New Zealand too suffered a top order collapse before Taylor steadied the ship with a 97-ball 64 that included six fours besides a six.
The Kiwis fumbled early in their chase as Shaun Tait trapped a scoreless Brendon McCullum with the second ball of the innings.
Bracken then removed Martin Guptil (13) and Mitchel Johnson caught Peter Fulton (7) off his own bowling to compound New Zealand's problems and Grant Elliot's (8) dismissal in the 23rd over left the visitors reeling at 64 for four.
The Kiwis found their saviour in Taylor who added 42 runs with Neil Broom (29) and another 62 with Mills (26) before another batting collapse. In the end, Vettori ensured his side ended up on the right side of the edge-of-the-seat thriller.
Mills was adjudged Man of the Match for his all-round show.
Both the teams now move to Melbourne for the second ODI on Friday.
Earlier, Ponting was left to regret his decision to bat first as Australia's top order crumbled in the face of New Zealand's spirited bowling and fielding. It was an abject batting display by the star-studded Australians and their first 54 runs cost them the entire top half of the batting line-up.
The 61-run stand between Hussey and Haddin arrested the slide for a while but Hussey's departure triggered another collapse and Australia could not even bat the entire 50 overs.
Much was expected from their exciting opening pair of Shaun Marsh (15) and David Warner (7) but Mills struck in successive overs with Fulton pouching both the batsmen at short cover.
There was an uncanny similarity in the next two dismissals as well as both Ponting (5) and his deputy Michael Clarke (12) ran themselves out.
And when David Hussey's (13) fluffed paddle-pull off Jetan Patel was pouched by McCullum behind the stumps, Australia clearly were in dire straits.
Hussey and Haddin then started the rebuilding job. Haddin started with a straight six off Patel and was going strong> when Mills struck again to remove the Australian.
Iain O'Brien then chipped in claiming the crucial wickets of Hussey and that unhinged Australia who lost the remaining wickets in quick succession to fold with eighth balls to spare.