The only resistance came in an entertaining 68-run stand for the fourth wicket in just 6.4 overs from Sabbir Rahman (48) and Soumya Sarkar (39) but that was Bangladesh's lot.
The innings was highlighted by a spectacular diving catch by Mitchell Santner at long on, running and hurling himself to his right to dismiss Mossadek Hossain.
Kane Williamson served up a half tracker and should be buying his young allrounder a meal tonight.
It was a bad day for New Zealand wicketkeeper Luke Ronchi.
He was out first ball of the match, spearing a catch to backward point, then strained a groin muscle early in Bangladesh's innings and had to be replaced.
Earlier, man of the match Munro and newbie Tom Bruce shared an innings-reviving stand of 123 in just 11.1 overs after Bangladesh had done a good early job, having won the toss and sent New Zealand in.
It is the second best fourth wicket stand in T20 cricket, behind Glenn Maxwell and David Warner's 161 against South Africa.
New Zealand lost Ronchi, captain Kane Williamson and Corey Anderson in quick order, to be 48 for three.
However Munro went on the offensive and found a good ally in the tall, muscular Bruce, who finished on an impressive unbeaten 59 off 39 balls.
Bangladesh were unable to stem the run flow and the batsmen went on a tear.
At one point, Munro scored 39 runs in just nine balls in the course of the 12th and 13th overs. His century means New Zealand have scored more international T20 hundreds than any other country.
Bangladesh's fielding got ragged as the runs piled on. Fast-medium Rubel Hossain was the most successful of the tourists' bowlers with three for 37. Shakib al Hasan and Mustafizur Rahman were the pick of them.