Kiwi captain Tom Latham’s superb innings of 65 off 49 deliveries went in vain as Tiger spinners restricted the visitors.
Shakib Al Hasan and Mehadi Hasan bagged two wickets apiece while Nasum got one.
Earlier, opener Mohammad Naim scored a run-a-ball 39 as Bangladesh posted 141 for six.
Naim and Liton Das (33) put on 59 for the first wicket after Bangladesh elected to bat first on the slow wicket.
New Zealand clawed their way back thanks to spinner Rachin Ravindra, who claimed two wickets in two balls before finishing with 3/22.
Bangladesh skipper Mahmudullah remained unbeaten on 37 to boost his side’s score.
Bangladesh had won the opening match by seven wickets at the same venue Wednesday.