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.
Taylor helped push the scoring on with Munro but had only contributed 28 to the total when tried to slog a full toss from Zaiur Rahman, only succeeding in edging to Naeem Silam at cover.
New Zealand then lost Corey Anderson for 18 and Luke Ronchi for a duck as they both looked to push on the total with Munro.
Anderson got an inside edge on to a full delivery from Al-Amin Hossain and Ronchi fell two balls later to the same bowler whose slower delivery saw the batsman return a catch to the bowler.
The returning Southee claimed the wicket of Shamsur Rahman off the second ball of the Bangladesh innings with the total on four.
Rahman had hit the first ball for a boundary but when the batsman went down the pitch to the next ball he flicked it to Mitchell McClenaghan on the long leg boundary.
Two balls later Mominul Haque gave a chance to second slip which Taylor could not hold on to.
Rahman opened up with a six off his first ball faced but the next from Southee, the last of the opening over, was a perfect yorker to claim his wicket and leave the home side on 11 for two.
Bangladesh lost their third wicket in the third over when Mominul (nine) top-edged to Kyle Mills at mid-on with the total on 19 for three.
The home side had put on 43 runs when Naeem fell for 18 as he ballooned a Mills delivery over mid-wicket but Southee ran backwards to take the catch.
Mushfiqur Rahim hit 50 as he put on 54 with Hossain but when the latter fell for 28 Bangladesh were 120 for six.
Gazi was run out for 23 leaving the home side needing 28 runs with two overs remaining.
But with Mahmudullah falling for 34 and Razzak for a duck Bangladesh were beaten by 15 runs after finishing their 20 overs short of their target.
- Sports & Recreation
- Shamsur Rahman
- Tim Southee
- Mushfiqur Rahim
- Ross Taylor
- Nasir Hossain