Chasing a revised target of 103 in a 15-over contest, New Zealand recovered from an early wobble to reach 104/4 in just 11.4 overs, with 20 balls to spare.
Bevon Jacobs led the charge with a blistering unbeaten 62 off 31 balls, striking five fours and three sixes, while Dean Foxcroft supported him with an unbeaten 15.
Bangladesh made a promising start with the ball as Shoriful Islam struck three early wickets to reduce the visitors to 33/4 inside five overs.
He finished with impressive figures of 3 for 19. However, the fifth-wicket partnership between Jacobs and Foxcroft turned the game decisively in New Zealand’s favour.
Earlier, Bangladesh were bowled out for 102 in 14.2 overs after being put in to bat. Towhid Hridoy top-scored with 33, while captain Litton Das made 26. Despite a steady platform, the hosts suffered a late collapse, losing wickets in quick succession.
New Zealand’s bowlers kept things tight throughout, with Josh Clarkson starring with 3 for 9. Nathan Smith and Ben Sears claimed two wickets each.
With the second T20I washed out without a ball being bowled, the series ended level at 1–1.