Williamson was out for 12 trying to hit wily spinner Shakib al Hasan, followed quickly by fellow Mount Maunganui homeowner Corey Anderson who hit his first ball for four but missed the third to be clean bowled by Shakib.
However Munro kept blazing away, bringing up his 50 in the 11th over off 31 balls and his 100, including seven sixes, off 52 balls - the third fastest by a Kiwi after two Brendon McCullum specials.
Munro and Bruce put on 123, with Bruce living up to his reputation as one of the best ball strikers in the country, making an unbeaten 59 off 39 balls.
Munro was happy with how the Bay Oval pitch played.
"Looking at it [Thursday] we thought it could be a little bit dry and be a little bit slow. We thought it might be like the practice wickets where it was hard to strike on but yeah the ball came on quite nicely I thought today," he said.
"My role in the team is to go out there and be aggressive but not be reckless at the same time. It is sort of a fine line sometimes. Today I thought I played really well."
Bangladesh's chase started poorly, with Mitchell Santner snaring opener Imrul Kayes for a duck in the opening over.
Local boy Trent Boult opened from the port end but conceded 10 runs to the flashing blade of Tamim Iqbal, who departed in the fourth over run out by a sharp Williamson throw with the total at 34-2.
It got worse next over when the highly regarded Shakib was out meekly to Ben Wheeler for one.
Black Caps then lost keeper Ronchi after he tweaked a groin muscle in the eighth over, with Bruce taking the gloves.
Soumya Sarkar and Sabbir Rahman put on 50 to push the chase at nearly 10 runs an over to 91-3 off nine overs. But again, with a win in sight, Bangladesh imploded.
Boult came back to remove Sarkar to break the crucial partnership of 68, then Rahman hit Ish Sodhi straight down Boult's throat for a well-made 48 off 32 balls.
Spinners Sodhi (3-36), Williamson (2-16) and Santner (1-14) then bowled tidy spells to finish off the disappointing Bangladesh innings.
Bay Oval was the perfect setting for the holiday crowd of 8000 fans packed in, with the overhead drone providing brilliant footage sent around the world - the estimated television audience in Bangladesh alone was 100 million.
The final game of the Twenty20 series is at Bay Oval from 3pm tomorrow.