After rolling New Zealand for 98 in 31.4 overs, captain Najmul Hossain Shanto made an unbeaten 51 from 42 balls and Amanul Haque 37 from 33 to lead Bangladesh to their first ODI win over the Kiwis in New Zealand in 19 attempts.
New Zealand won the three-match series 2-1 after claiming the first match by 44 runs and the second by seven wickets.
But Bangladesh gained a measure of revenge on Saturday and primed themselves for the upcoming T20 series, bowling New Zealand out for their lowest ever total in ODIs between the teams.
Bangladesh's Soumya Sarkar (left) claims the wicket of New Zealand's Adam Milne (right). (AP PHOTO)
Earlier, Tanzim Hasan Sakib took 3-14 and Shoriful Islam 3-22 - both career bests - as Bangladesh rolled New Zealand cheaply to set up a dominant victory.
Soumya Sarkar chipped in with 3-18 as New Zealand fell below their previous lowest ODI score against Bangladesh of 162.
"The ball was nipping, the ball was swinging and I knew how we started would set the tone for my team," Sakib said.
"I tried to bowl wicket to wicket and hold my line and length.
"The wicket really helped me. This wicket is good for pace bowlers and the wicket really helped me."
Bangladesh captain Shanto was delighted to be able to choose to field when he won the toss.
The McLean Park pitch usually is one of the best to bat on in New Zealand, with an average first-innings score in ODIs of 239.
But the pitch was unusually well-grassed and Shoriful and Sakib took full advantage, crashing through the New Zealand top order to leave the hosts reeling at 6-70.
Both bowlers tied the New Zealand batters down by bowling into the stumps and swinging the ball both ways.
They hit excellent lengths and the ball occasionally spat off a length, which made the batters reluctant to play forcefully off the front foot.
The largest partnership in the innings was 36 between Will Young (26) and Tom Latham (21) for the third wicket.
Only two other New Zealand batters reached double figures.
Shoriful reproduced the form that saw him take two wickets in the opening over of the first ODI, dismissing Young, Latham and Mark Chapman (2).
Both Latham and Chapman were bowled by deliveries that jagged back late between bat and pad.
Sakib maintained an exacting line, giving the batters no width and completing two maidens among his seven overs.
He dismissed Rachin Ravindra (8) in the fourth over to begin the New Zealand collapse, then removed Henry Nicholls (1) and Tom Blundell (4).
When the two seamers had left the hosts' innings in tatters, Sarkar came on and took the wickets of Josh Clarkson (16), Adam Milne (4) and Adithya Ashok (10).
The last wicket fell to Mushfiqur Rahim (1-36).
