Vettori slayed 70 off 49 balls as New Zealand chased a rain-reduced target of 266 off 45 overs, but was bowled around his legs by Ryan Harris as the hosts were dismissed for 253 with 10 balls remaining at Eden Park.
It was yet another pulsating Chappell-Hadlee finish as the sides go to Hamilton on Tuesday poised at 1-1 in the five-match series.
New Zealand were always behind in their runchase and when Vettori arrived at the crease they were 131 for six in the 27th over.
He hit the ball to all parts as Gareth Hopkins and Daryl Tuffey chipped in, reaching just his fourth one-day half-century in his 252nd match, off 34 balls as the crowd of 13,500 sensed another upset.
When New Zealand took the power play they needed 26 off 24 balls and they looked a huge chance when Vettori hit Mitchell Johnson for consecutive boundaries.
But with last man Tim Southee at the crease, Vettori shuffled across his stumps one time too many.
Villain-of-the-moment Johnson took four for 51 with the ball as the crowd taunted him constantly, while Harris was impressive with three for 34.
There were more New Zealand injury dramas, with Ross Taylor a late withdrawal due to a hamstring strain suffered in the opening game in Napier.
A pained Vettori looked highly doubtful, having not batted or bowled yesterday, but he bit the bullet when Taylor was scratched.
Hopkins was whistled up to take the gloves due to Brendon McCullum's sore back, then James Franklin strained his hamstring while bowling and limped off.
New Zealand's chase only spluttered into gear as Johnson and Harris ripped through the top order as they slumped to 46 for four.
McCullum hit two sixes in a quickfire 24 before Johnson removed him thanks to a brilliant one-handed Brad Haddin catch.
Harris dismissed Peter Ingram and promoted No 4 Neil Broom in successive balls, then Franklin, with Broom as his runner, had his unhappy day ended when he was caught down the leg side for two.
With the crowd roaring, Johnson resumed his duel with Scott Styris with a bouncer which soared for five wides then was cracked for four twice more in the over.
Styris was in control but his 46 off 58 balls ended with a soft dismissal, chipping a catch off spinner Nathan Hauritz, and Hopkins hit 35 off 39 before he departed to a wild hook shot, leaving Vettori as the last hope.
After winning the toss, Australia's innings was almost a carbon copy of their effort in Napier as they looked poised for 300-plus but were hauled back by senior men Vettori and Shane Bond.
Vettori struck with his fifth ball, the prized wicket of Ricky Ponting for one, and also removed Haddin for 53 to a sharp one-handed caught and bowled to end with two for 43.
Bond, who took two for 42, was his usual sharp self as he dismissed topscorer Michael Hussey for 56 and an out-of-sorts Michael Clarke for 11, but Southee, Tuffey and Franklin were expensive.
Franklin injured himself in the process of removing Cameron White, caught in the deep for 54, and he couldn't complete his fifth over.
Hussey's second consecutive half-century saw his average in 12 one-dayers in New Zealand drop to 96.40. He lifted Australia from a shaky 116 for four as he and White added 101 for the fifth wicket.
