The hosts benefitted from a mid-innings flourish, anchored by Neil Broom's maiden ODI century of 109 off 107, but regular wickets meant full throttle could never be reached.
Broom and Jimmy Neesham (28 off 31) added 51 for the fourth wicket off 58 balls, followed by 64 off 72 balls with Luke Ronchi (35 off 38) for the sixth wicket. It was Ronchi's highest score in 10 ODI innings.
Elsewhere, continuity was fleeting. Trent Boult's cameo of 12 off as many balls at No 11 saved their blushes. They were the second side in 13 completed innings to be bowled out at the venue, but at least used up their overs.
Saxton Oval is the only ground where Bangladesh have won an international in New Zealand, defeating Scotland by six wickets at last year's World Cup.
On that occasion they hauled in 319 to win, the highest chase at the venue. This time the task looks less daunting. The Black Caps will need to act out a dramatic bowling and fielding script to challenge history.
Five of the six completed ODIs at the venue have seen the chasing team haul in anywhere between 277 and 319. The exception was New Zealand beating the West Indies by 58 runs via the Duckworth-Lewis Method in 2014. Rain looks unlikely today.
Captain Mashrafe Mortaza galloped to the crease like it was the finishing post in the Melbourne Cup and, after getting denied an lbw review against Martin Guptill third ball, trapped him next delivery.
He went on to lead the bowling figures with three for 49 from his allotment.
That set the tone in combination with tenacious fielding. Debutant wicketkeeper Nurul Hasan's set an example with his clinical stumping of Jimmy Neesham and sharp catch of Tim Southee standing up to the stumps. His contribution was reinforced by the fieldsmen. Strokes into the outfield were chased as if a bank note was getting blown down the street. No more than seven runs were taken from any of the first 30 overs.
Other bowlers contributed tidy spells. Taskin Ahmed's two for 45 was a highlight which included two overs at the death.
A 23-ball spell between the eighth and 11th overs stung the hosts. Two runs were scored - one was a wide - and Kane Williamson was dismissed.
The captain personified the difficulties faced by the New Zealand batsmen. He struggled to get comfortable. Bangladesh used the clever tactic of bowling on middle-and-leg, looking for him to glance into the hands of leg slip. Two boundaries were the result, but the balls went in the air.
Williamson escaped a caught-and-bowled chance on 13 in the eighth over as debutant Subashis Roy threw a hand to his right in the follow-through. Taskin, who had Williamson caught behind at Christchurch, forced a shot four dot balls in the 11th over with the No 3 on 14. The ball lobbed to Shakib Al Hasan at mid-on.
