Stand-in skipper Najmul Hossain Shanto scored 76 runs but New Zealand restricted Bangladesh to 171 in the series-deciding third and final one-day international in Dhaka on 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 New Zealand wrap up the Bangladesh innings in 34.3 overs.
The bowling performance gave New Zealand 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.
The Kiwis are leading the series 1-0 thanks to their 86-run win in the second match on Saturday. The first match was washed out by rain.
Bangladesh initially rested key players but, with the series at stake, they brought back stalwarts Najmul, Mushfiqur Rahim and Shoriful Islam. However, it did little to improve their performance.
Bangladesh won the toss and elected to bowl first.
Najmul, 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 Najmul and Mushfiqur offered a brief resistance with a 53-run fourth wicket stand.
Mushfiqur'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 Najmul 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.
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