Munro returned unbeaten on 73 off 39 balls to lift New Zealand to their second-highest total in T20 cricket behind the 214-6 against Australia in 2010.
Munro, a 26-year old left-hander, entertained the crowd at the Sher-e-Bangla stadium with three fours and five sixes.
Debutant Devcich had given the tourists a flying start with 59 off 31 balls before he fell to left-arm spinner Abdur Razzak.
Bangladesh rued their poor catching as debutant Al-Amin Hossin dropped Devcich off Mashrafe Mortaza on six in the first over of the innings.