Batting at number three, Mahedi Hasan departed for only 1 and Shakib Al Hasan went for a duck. Both lost their wickets in the fourth over and first over bowled by Ajaz.
Captain Mahmudullah and Afif Hossain fell prey to Ajaz in successive deliveries of 10th over leaving Bangladesh on 43 for six.
Nurul Hasan joined senior player Mushfiqur Rahim but failed to make any impact with bat as he holed out in long on for 8 off 11 balls.
Mushfiqur played till the last but could never rekindle the Tigers’ hope to chase the total. He could not produce any boundary in his struggling innings of 20 off 37 balls not out.
Ajaz Patel scalped 4 important wickets conceding only 16 runs and adjudged player of the match. Cole McConchie bagged 3 wickets for 15 while Rachin Ravindra, Colin de Grandhomme and Scott Kuggeleijn got one each.
Earlier after electing to bat first, New Zealand posted 128 for five in 20 overs, thanks to an unbeaten 66-run sixth wicket partnership by Henry Nicholls and Tom Blundell after the visitors lost five wickets for 62.
Nicholls was unbeaten for 36 off 29 balls and Tom Blundell at a run-a-ball 30.
Mohammad Saifuddin bagged 2 wickets while Mahedi Hasan, Mahmudullah and Mustafizur Rahman got one wicket each.
Bangladesh beat New Zealand by 7 wickets and four runs in the first two matches.
Next two matches will be played at the same venue on 8 and 10 September respectively.