Mitchell Johnson took 4-20 off four overs to restrict the New Zealanders to a total of 147, and Australia reached 151 for three with four balls to spare, thanks to a 104-run stand between captain Ricky Ponting and his deputy, Michael Clarke, for the third wicket.
Ponting hit 56 off 38 balls, including two sixes and five fours to top score, while Clarke finished not out 49, accompanied by Andrew Symonds, who was not out 17.
New Zealand won the toss and elected to bat, but lost openers Brendon McCullum and Jesse Ryder each for no score, thanks to Brett Lee on the third ball of the match and Johnson with his second delivery in the following over.
Johnson claimed another wicket three balls later when Martin Guptill spooned a catch straight to Nathan Hauritz at mid-on and New Zealand were in desperate trouble at six for three.
The Black Caps' problems deepened as they collapsed to 21 for five inside the first six overs.
But Scott Styris and Peter McGlashan finally stopped the haemorrhage of wickets with a 71-run partnership off 45 balls.
McGlashan said afterwards that the top order collapse had been of unexpected benefit.
"(Australia) got the result, but there are definitely positives we can take out of it," he said. "Our top order's done reasonably well in the warm-up games up until now, so for the lower order to get tested is probably a good thing long-term."
Styris piled on 24 runs off eight consecutive balls before he was caught behind by Brad Haddin off Johnson for 42, reached off 28 with two sixes and four fours.
McGlashan fell one run shy of his half century when he was caught by David Hussey off Hauritz.
In his first match against Australia, McGlashan said the benefits of having Styris at the other end had been enormous.
"He's got a huge amount of experience, so it was good to have him out there. He's obviously played against Australia plenty of times, and it was my first time against them so to have him there at the other end was a calming influence."
McGlashan said he was "as relaxed as you can be, facing Australia for the first time", but the pressure had still been on after the top-order failed to perform.
"We've been talking all along through the campaign that we've got enough ball strikers that we can just continue to go for the whole 20 overs.
"But when you're 21 for five, that kind of stretches that theory a little bit."
McGlashan has made the most of a surprise call-up to the squad, and was happy to have had the chance to show what he could do at No 7.
"It was nice to take the opportunity -- it was one of those situations where I had nothing to lose. We were in a fairly precarious position, so to do well and take advantage of that was nice."
The Black Caps began their warm up for the tournament, which starts early Saturday (NZT), with a nine-run victory over India at Lord's in London yesterday.
