Set a modest target of 258, a fifth wicket stand of 80 between Neil Broom and Jimmy Neesham proved a match-winning one.
Although Broom fell two runs short of his second 50 of the series and Neesham followed him back to the pavilion immediately after reaching the landmark, there was no late scare for this impressive Black Caps side
After Luke Ronchi had given New Zealand their usual fast start (27 from 27 balls) skipper Tom Latham led from the front with 54 from 64 balls.
When he was dismissed in the 21st over, they were already scoring at the required run-rate and although Ross Taylor was leg before to Mustafizur Rahman for 25, Broom and Neesham regained the momentum which put them firmly in control.
Rahman and Rubel Hossain each took two wickets but the Bangladesh bowlers just did not have enough runs to play with on the compact Clontarf ground.
Bangladesh managed only 257 for nine despite three batsmen making half centuries.
Soumya Sarkar, Mushfiqur Rahim and Mahmuduallah all reached 50 but none could go on and Sarkar ended up as the top scorer with 61.
Hamish Bennett, the one change in the Black Caps line-up which beat Ireland in their first match on Sunday -– he replaced Scott Kuggeleijn -– was rewarded for an economical 10-over spell with two wickets in the last over to finish with three for 31.
Bangladesh also had to had make one change to their first line-up with captain Mashrafe Mortaza, who had been suspended for the Ireland game last Friday, returning in place of Taskin Ahmed.
The Tigers enjoyed a bright start with Tamim Iqbal and Sarkar putting on 72 for the first wicket but they had lost two wickets by the first drinks break with Tamim caught on the cover boundary for 23 and eight balls later, Sabbir Rahman was bowled by Mitchell Santner, the Black Caps' five-wicket man of the match on Sunday.
Santner was even more economical on Wednesday, conceding just 36 runs, but that was his only wicket and it was Ish Sodhi was upstaged him with two for 40, ending Sarkar’s 67-ball innings which included just five boundaries.
Despite the short boundaries, Bangladesh struggled to find them with Mahmudullah the most successful, hitting six in his 51 while Mushfiqur hit the only six of the innings in his 55.
Mosaddek Hossain picked up the pace in the closing stages with a run-a-ball 41 (four boundaries) but it was New Zealand -– three places higher than Bangladesh in the rankings -- who were the happier at the break and the batsmen finished the job in some comfort.
The next match in the series is Ireland against Bangladesh at Malahide on Friday.