Debutant Josh Clarkson, Ish Sodhi and Adam Milne took a couple of wickets as the hosts won the match comfortably.
Chasing 245 runs in a rain-interrupted 30-over chase, Bangladesh lost 200-9 by 44 runs in Duckworth and Lewis method at Dunedin's University Oval on Sunday.
Anamul Haque hit a brisk 43 while Afif Hossain and Tohwid Hridoy made 38 and 33 respectively but neither of the three could convert their start into a big innings to take Bangladesh all the way,
Debutant Josh Clarkson, Ish Sodhi and Adam Milne took a couple of wickets as the hosts won the match comfortably.
Earlier, New Zealand posted 239-7 in 30 overs thanks to Will Young's third ODI ton and a 77-ball 92 from Tom Latham.