After drawing both Tests and losing the three one-day internationals the Black Caps signed off the tour by finally registering their first win.
All-rounder Munro scored 73 runs from 39 balls to help steer the Black Caps to 204 for five, Munro hitting five sixes and three fours as he put on a useful stand of 93 with Ross Taylor for the third wicket.
Bangladesh were 189 for nine in reply, Mushfiqur Rahim top-scoring with 50 and Tim Southee claiming three for 38.
New Zealand opener Hamish Rutherford was the first to fall after scoring 17 out of an opening stand of 73 with Anton Devcich.
Rutherford perished trying to lift Sohag Gazi for six but picked out Nasir Hossain on the long-on boundary.
New Zealand had only added a further 10 runs when Devcich fell for 59 off 31 balls, getting a top edge to Shamsur Rahman after trying to slog sweep Abdur Razzak.
Brief scores: New Zealand 204-5 in 20 overs (Colin Munro 73*, Anton Devcich 59; Al-Amin Hossain 2-31) beat Bangladesh 189-9 in 20 overs (Mushfiqur Rahim 50; Tim Southee 3-38) by 15 runs