Australia were all out for 191 in reply to New Zealand’s 246.
For New Zealand, Martin Guptill top scored with 59, Grant Elliott made 50 and Brendon McCullum 47.
For Australia, Usman Khawaja made 44 and Mitchell Marsh 41.
Bowling for New Zealand Matt Henry took three for 60.
The series now moves to Wellington for the first of two Tests starting on Friday.