Chasing 192 for victory in the Group D match, Mushifiqur Rahman's men ran out of steam and finished at 132 for 8. The Black Caps gave their Net Run Rate a big boost, which could be crucial in deciding which two teams go to the Super Eights.
Bangladesh, who have now lost nine consecutive T20Is, now need to beat Pakistan to have any chance of advancing from the group billed as the Group of Death.
Bangladesh's top-scorer Nasir Hossain was the only player to show some fight but did not get support. He made a gritty 50 off 39 before he tried to smoke Tim Southee and was caught brilliantly by Martin Guptill at long-on.
They were never in the contest once Tamim Iqbal (0) and Shakib Al Hasan (11) went back in the hutch cheaply.
Mahmudullah put on 50 runs with Nasir Hossain, and was looking good until he hit Nathan McCullum straight to Kane Williamson at long on for 15.
Mohammad Ashraful (21) perished with a big swing across the line and was adjudged lbw.
Kyle Mills picked up three wickets inside five overs to throw the Tigers out of the game. He returned Tamim in the very first over with the left-hander hitting straight to Guptill at cover
Shakib was foxed by a Mills slower from around the wicket and he chipped it to Williamson diving forward in the covers And then skipper Mushfiqur Rahim (4) attempted to hit big only to be caught out by Williamson at deep midwicket.
Earlier, a scorching 123, highest in T20Is, by McCullum helped his side rack up a massive 191 for 3 in their 20 overs.
The 30-year-old right hander lit up the stadium with the extraordinary onslaught for the highest individual score in a T20 international after Mushfiqur Rahim decided to bowl first with clouds around.
McCullum, caught off the final ball at the cover boundary by Tamim Iqbal off Abdur Razzak, hit wayward Bangladesh bowlers all around the park in his 58-ball knock that had only 10 dot balls. Skipper Ross Taylor remained unbeaten on 14.
McCullum became the first player to smash two T20I hundreds, off just 51 deliveries – one ball more than Chris Gayle of West Indies. His blitz included 11 boundaries and seven sixes and he also become the highest scorer for the Black Caps in World T20.
McCullum lofted Abdur Razzak for two sixes in the last over of the innings to go clear of South African Richard Levi's previous highest score of 117 made against New Zealand in Hamilton earlier this year.
Mashrafe Mortaza, who dropped McCullum on 92 in 18.1 overs, took out James Franklin (35), who pulled flat to Elias Sunny at deep midwicket. His 94-run second wicket effort with McCullum gave the Kiwis the platform to have a go in the later overs.
Left-arm spinner Razzak drew the first blood slipping one through the defence of opener Martin Guptill for 11.
