New Zealand was bowled out for 60 to equal their lowest Twenty20 total as Bangladesh won the first of their five-match series by seven wickets.
The visitors won the toss in Mirpur and opted to bat, but their top four fell for just nine runs.
Tom Latham and Henry Nicholls, both with 18, were the only players to score double figures.
Bangladesh lost both openers for one before Mushfiqur Rahim and captain Mahmudullah led them to victory.
New Zealand was last bowled out for 60 in their World Twenty20 defeat by Sri Lanka in Chittagong in 2014.
The second match in the series will take place at the same venue on Friday.