Munro hit five sixes in an innings which amply demonstrated his aggressive qualities and should have him shaping as an important figure in the home limited-overs programme against the West Indies and India.
The other key innings came from tyro opener Anton Devcich.
He hit 59 off just 31 balls to give New Zealand's innings a flying start. Munro and Ross Taylor then shared a rapid 93-run stand for the third wicket to set Bangladesh a target which was beyond them.
Their chase ended at 189 for nine, of which their inspirational captain Mushfiqur Rahim hit a quick maiden T20 50.
Bangladesh did give New Zealand a scare though, being narrowly ahead on comparative run rate as late as the 13th over.
However, they had lost too many early wickets and the tail was unable to complete the job, as Tim Southee, Mills and Corey Anderson played key roles with the ball.
Southee finished with three wickets, and Anderson two as a 10-game barren period in Bangladesh was brought to a halt.
New Zealand now head to Sri Lanka for three ODIs and two T20s, starting in Hambantota on Sunday.
No Brendon McCullum, Taylor or Kane Williamson - respectively at home receiving rehabilitation on a wonky back, preparing for the arrival of the West Indies, and recovering from a fractured thumb - means more chances for new players.
It also makes an already difficult challenge even harder against a strong Sri Lankan side.
''It's a great opportunity for a number of us to stand up," Mills said.
''The T20 World Cup is not long after Christmas (back in Bangladesh) and there's also the big World Cup in 15 months' time (in Australia and New Zealand).
''So it's an opportunity for us to get some solid performances before we get to our home summer."
