They had the hosts 41 for three, only to be bounced all around the park by Corey Anderson, who clobbered a New Zealand record 10 sixes in his unbeaten 94 off just 41 balls.
Anderson and captain Kane Williamson, with 60 off 57 balls, shared a New Zealand fourth wicket record of 124, eclipsing the two-day old mark of 123 set by Colin Munro and Tom Bruce on Friday.
Then chasing an improbable 195 to win, Bangladesh flew out of the gates, chiefly through Soumya Sarkar's 42 off 29 balls and were roaring at 69 at the end of the six-over power play.
Not a single boundary followed in the next seven overs and that was that.
Anderson sailed past the previous best New Zealand six-hitting effort, the eight of Brendon McCullum against Australia in Christchurch seven years ago. Only three players have hit more in a T20 innings and the crowd got full value for their money.
''It wasn't easy at times, you had to adjust to the wind," Williamson said. ''But it didn't matter for Corey.
''It was nice to be at the other end while he was hitting it to all parts."
Williamson was dropped twice, at 53 and 58, and had his struggles early on with timing and tidy bowling, but prospered through sticking it out. Anderson's was a compelling display, all power and clean striking.
The key period was the third block of five overs. New Zealand had laboured to 55 for three after 10 overs; the next five went for 70.
Bangladesh were in the wars in the field. Imrul Kayes went sprawling over an advertising hoarding trying to catch one of Anderson's sixes and headed for the pavilion; captain Mashrafe Mortaza went for a scan after his hand bore the brunt of another Anderson howitzer in his followthrough.
Anderson would almost certainly have nailed the fastest T20 century - 45 balls by South African Richard Levi against New Zealand in Hamilton five years ago - only to run out of balls. He had three up his sleeve and six runs needed at the end of the innings.
He was determined not to hang about without making an impact with the likes of other heavy hitters back in the pavilion. There was no fear of that.