A knock of 137 off 121 balls from Black Caps opener Tom Latham helped them set an imposing target of 342 runs to win for Bangladesh in the first ODI at the Hagley Oval.
Bangladesh would ultimately be bowled out for 264 to lose the series opener by 77 runs with Jimmy Neesham and Lockie Ferguson picking up three wickets apiece.
Earlier Mustafizur Rahman got the initial breakthrough for the Tigers removing Martin Guptill for 15 when New Zealand were on 31.
Kane Williamson (31), Neil Broom (22) and Neesham (12) failed to make the most of solid starts but Latham kept going from the other end until Colin Munro joined him in the middle.
Latham and Munro added 158 for the fifth wicket with the latter eventually departing for a well played 87.
The left-handed opener would depart shortly afterwards in the pursuit of a big finish and Luke Ronchi would miss a full one from Taskin Ahmed to leave New Zealand 327 for 7 in the penultimate over.
Mitchell Santner and Tim Southee helped the Black Caps to 341 in their fifty overs.
The Tigers response was plagued by the steady loss of wickets with Southee accounting for Imrul Kayes (16) before Neesham picked apart the top order with three wickets.
Soumya Sarkar (1), Mahmudullah (0) and Tamim Iqbal (38) all fell to the allrounder as the Tigers limped to 81 for 4.
Shakib-al-Hasan and Mushfiqur Rahman looked to be steadying the ship for Bangladesh before the former holed out to Ferguson for 59.
Sabbir Rahman (16) was the next victim of Ferguson and just like Shakib he had struck the rapid Black Caps bowler for six the ball before.
Just as Mosaddek Hossain and Mushfiqur were getting going the latter was forced to retire hurt with the tigers on 219 for 6 in the 39th over.
With that Bangladesh would slide to 264 all out, Mosaddek would end unbeaten on 50 as New Zealand secure a 1-0 lead in the three-match series.