With this win, Bangladesh are leading the series 2-0.
The match was originally scheduled for Wednesday but had to be rescheduled due to rain.
New Zealand won the toss and opted to bat first. They put up 142 for six wickets with the help of Thomas Zohrab (112). Besides him, Ollie White scored 30.
For Bangladesh, Mrittunjoy Chowdhury took two wickets conceding 41 runs in seven overs.
In reply, Bangladesh scored 243 for four wickets in 46.3 overs and won the game by six wickets.
Mahmudul Hasan Joy scored 99 while opener Tanzid Hasan posted 65 to guide the young Tigers to the second successive win.
For New Zealand, Jock McKenzie took two wickets for 39 runs in seven overs.
The remaining matches of the series, scheduled for Oct 6, 9 and 13, will be played at the same venue.