Chasing a target of 195 Bangladesh could only manage to score 167 for the loss of six wickets. Soumya Sarkar (42) and Shakib Al Hasan (41) were the top scorers for the guests.
Corey Anderson and Kane Williamson blasted half centuries as New Zealand overcame early jitters to post 194 for 4 batting first at Mount Maunganui.
Anderson's unbeaten 94 off just 41 balls included a New Zealand record 10 sixes while Williamson was out for 60 off 57 balls as they put on 124 for the fourth wicket.
They came together with New Zealand in trouble at 41-3 having lost three wickets for seven runs in 11 balls.
The Williamson-Anderson partnership took time to settle with New Zealand reaching the halfway stage with only 55 on the board before they went on the attack and bludgeoned 139 runs off the last 10 overs.
For Bangladesh, Rubel Hossain took three for 31 while captain Mashrafe Mortaza had to leave the field injured and could not complete his fourth over.
With this series loss, Bangladesh remained winless on New Zealand tour.