Having won the toss, Australia skipper Steve Smith put the hosting Kiwis into bat, and it was a decision that soon backfired as the opening pair of Martin Guptill and Brendon McCullum scored 90 and 44 runs respectively.
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However, Guptill was then joined at the crease by Henry Nicholls (61) and they put together a 100-run partnership for the third wicket to steady the innings.
The New Zealand tail also made some useful contributions, most notably Mitchell Santner, who added an unbeaten 35 to help his team reach 307-8 from their 50 overs.
In response, the tourists collapsed as their first six batsmen were removed for a score of 41-6, having been 33-1 at one point. They could not handle the pace of Trent Boult and Matt Henry, who helped themselves to three wickets apiece.
Matthew Wade top-scored with 37, but it did little to prevent the Aussies from being bowled out for 148 inside 25 overs.
The teams will meet again on Saturday when New Zealand will have the opportunity to wrap up a series victory in Wellington.