Stand-in skipper Nazmul Hossain Shanto scored 76 runs but New Zealand restricted Bangladesh to 171 in the series-deciding third and final one-day international in Dhaka Tuesday.
Adam Milne picked up 4/34 while playing his first match of the series, with Cole McConchie and Trent Boult claiming 2/18 and 2/33 respectively to help the Kiwis wrap up the Tigers innings in 34.3 overs.
The bowling performance gave the Black Caps a boost in their pursuit of their first series win in Bangladesh in 15 years, having lost the previous two series 4-0 in 2010 and 3-0 in 2013.
New Zealand are leading the series 1-0 thanks to their 86-run win in the second game Saturday.
The first match was washed out by rain.
The men in red and green initially rested key players but, with the series at stake, they brought back stalwarts Shanto, Mushfiqur Rahim and Shoriful Islam.
Liton Das, who led in the first two games, was rested while Tamim Iqbal, Soumya Sarkar, and Mustafizur Rahman were left out.
New Zealand handed over an ODI debut to Dean Foxcroft for Chad Bowes, and brought Milne for Kyle Jamieson in their two changes.
Bangladesh won the toss and elected to bowl first.
Shanto, leading Bangladesh for the first time, held down one end to score his fifth ODI fifty but wickets kept falling regularly from the other end.
Milne and Boult struck early to reduce Bangladesh to 35/3, before Shanto and Mushfiq offered a brief resistance with a 53-run fourth wicket stand.
Mushfiq's dismissal to Lockie Ferguson for 18 put New Zealand back on top and the visitors did not lose the momentum again.
McConchie ended any real chance of Bangladesh lodging a fighting score by dismissing Shanto with his second ball of the day, with the left-hander hitting 10 fours in his 84-ball innings.
The match is the last for both teams before the World Cup starts in India on October 5.
