Litton Das surprised all by attempting a big shot off a short ball and was caught out on the very first delivery of the inning. Within a mere 40 runs, Bangladesh lost Tanzid Hasan Tamim as well.
New Zealand captain Kane Williamson returned to the team to play his first match at the World Cup in Chennai on Friday, winning the toss and opting to bowl first against Bangladesh.
Williamson sat out New Zealand's opening two wins as he recovered from a knee injury but was named in the starting line-up in place of Will Young.
The 33-year-old Williamson has scored 6,554 runs in one-day international cricket at an impressive average of nearly 48.
Bangladesh opened their World Cup campaign with victory over Afghanistan before losing to defending champions England.
They have recalled Mahmudullah in place of Mahedi Hasan.
Bangladesh
Liton Das, Tanzid Hasan, Najmul Hossain Shanto, Shakib Al Hasan (capt), Mehidy Hasan Miraz, Mushfiqur Rahim (wk), Towhid Hridoy, Mahmudullah, Taskin Ahmed, Shoriful Islam, Mustafizur Rahman
New Zealand
Devon Conway, Rachin Ravindra, Kane Williamson (capt), Daryl Mitchell, Tom Latham (wk), Glenn Phillips, Mark Chapman, Mitchell Santner, Matt Henry, Lockie Ferguson, Trent Boult