The New Zealand cricket captain Daniel Vettori paid Bangladesh due credit after the Black Caps' humiliating loss in the opening one day international in Mirpur.
The home side won a vital toss on a pitch drenched by overnight rain, and while the NZ openers Jessie Ryder and Brendon McCullum put on 47 runs for the first wicket, McCullum's dismissal sparked a dramatic collapse as they lost six wickets for 32.
Chasing 202 for victory, Bangladesh reached their target in the 46th over with seven wickets in hand.
Vettori said once the pitch dried out, 201 was never going to be enough.
It was Bangladesh's first one-day win over New Zealand, though they did beat the Black Caps in a World Cup warm-up match last year, and went on to win four games in the tournament proper.