After being sent in to bat first, New Zealand were 307-8 after their 50 overs with Martin Guptill making 90 and Henry Nicholls 61.
Australia in reply were all out for 148 in the 25th over.
Matthew Wade top-scored for the tourists with 37 while for New Zealand’s Trent Boult took three for 38 and Matt Henry three for 41.
The second game in the three-match series takes place in Wellington on Saturday.
New Zealand strike bowlers Trent Boult and Matt Henry destroyed world champions Australia and set up a comprehensive 159-run victory in their opening one-day international in Auckland on Wednesday.
In reply to New Zealand’s 307-8, Australia were all out for 148 in the 25th over.
New Zealand, sent in to bat, made an aggressive start with Martin Guptill (90), Henry Nicholls (61) and Brendon McCullum (44) getting them past the 200 mark in 30 overs.
The run rate slowed with the tailenders but a total in excess of 300 at Eden Park, even with its short boundaries, was competitive.
Australia were never seriously in contention with their reply.
Their innings began to unravel at the very start as Henry and Boult ripped out the top order to have the tourists reeling on 41-6 after nine overs.
Henry, a surprise omission from the New Zealand team for next month’s World Twenty20 championships, continued the form that made him New Zealand’s leading bowler in their recent series wins over Sri Lanka and Pakistan.
