The Tigers triumphed by five wickets with 10 balls to spare at Dublin, hauling in the highest chase in 21 completed ODIs at the Clontarf ground.
The key element was an unbeaten 72-run sixth-wicket partnership between Mushfiqur Rahim (45 from as many balls) and Mahmudullah (46 from 36). The result moves Bangladesh to sixth in the world rankings. A rematch set between the sides is set for June 9 at Cardiff in the Champions Trophy.
Bangladesh's composure, on the back of a 136-run second-wicket stand between Tamim Iqbal (65 off 80 balls) and Sabbir Rahman (65 off 83 balls) saw them to victory after sending New Zealand in.
The haul was not without its stumbles. The Black Caps took three wickets for 17 runs in as many balls between the 27th and 30th overs. The required run rate fluttered above six but never reached heart palpitation levels.
The Bangladeshi batsmen hardly had to swing like bushmen with machetes at the death.
New Zealand were let down by middle order batting which stifled the momentum created by the 133-run second-wicket stand between Tom Latham (84 off 92) and Neil Broom (63 off 76). Their bowlers could not defend the subsequent total for any sustained period. The result raised questions over their penetration.
The Black Caps went from 208 for three in the 39th over to 226 for seven in the 44th.
With Corey Anderson's dismissal for 24, they lost four wickets for 18 runs in 27 balls as Jimmy Neesham, Mitchell Santner and Colin Munro also exited.
The batting capability of their all-rounder contingent will come under scrutiny against the likes of Australia and England next month.
Ross Taylor knitted the innings into a competitive total with a senior pro's 60 from 56 balls - the only New Zealand batsman to go at better than a run a ball.
The Bangladesh bowlers fought back in later spells. Off spinner Nasir Hossain removed Latham and Broom to finish with two wickets for 47 runs from nine overs. He was backed by Mashrafe Mortaza's 2-52, Shakib Al Hasan's 2-41 and gritty death bowling from Rubel Hossain and Mustafizur Rahman.
The Tigers' biggest weakness was fielding, including four dropped catches. Latham was dropped on nought by Nasir at square leg off Mashrafe in the first over.
That was followed by an escape on 50 from a lobbed caught-and-bowled. Bowler Mosaddek Hossain claimed to have been obstructed by non-striker Broom. The decision was referred to the television official by umpire Roly Black. Broom was declared not guilty.
New Zealand at least remained consistent with the bat across the series. In this match they were saved by the tempo and platform built by Latham's crisp strokes, particularly square of the wicket.
Solid opening powerplays of 57-2 (Ireland), 48-1 (Bangladesh), 70-0 (Ireland) and 60-1 (Bangladesh) were backed by resolute middle 30-over blocks of 145-2, 156-3, 152-3 and 157-3, which bode well for the Champions Trophy.
A saving grace was the fact today's Black Caps side will bear little resemblance to that which takes the field in the tournament proper once the Indian Premier League contingent of Trent Boult, Colin de Grandhomme, Martin Guptill, Mitchell McClenaghan, Tim Southee and Kane Williamson are considered for selection.
