Electing to bat after winning the toss, the hosts rode on opener Tom Latham's superb 137 and all-rounder Colin Munro's quickfire 87 to post a stiff 341 in their 50 overs.
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In reply, Bangladesh could only blame their poor shot selection and execution to be bowled out for 264 in 44.5 overs, on a batting-friendly pitch.
Earlier, Latham, who smashed a 121-ball 137 forged a 158-run fifth wicket stand with Munro to take the hosts to the massive score.
Opening the innings with Martin Guptill (15), Latham set the platform with a 31-run stand before adding another 48 for the second wicket with skipper Kane Williamson (31).
The southpaw, whose innings was laced with seven fours and four huge sixes, then went on to add another 55 runs for the third wicket with Neil Broom (22) before being joined by Munro.
Munro went ahead playing his natural game to get to his score in just 61 deliveries and contained eight hits to the fence and four over it.
For the visitors, all-rounder Shakib Al Hasan was the pick of the bowlers with figures of 3/69 while the pace duo of Mustafizur Rahman and Taskin Ahmed took two wickets apiece.
In reply, Bangladesh got off to a brisk start with openers Tamim Iqbal (38) and Imrul Kayes (16) yielding 34 runs before being pulled back with three quick wickets.
Shakib (59) and wicketkeeper-batsman Mushfiqur Rahim (42 retired hurt) then resurected the innings with a 63-run fifth wicket stand to take the visiting side to 144 before the southpaw was dismissed by Lockie Ferguson.
Rahim, however went ahead and added another 52 runs for the seventh wicket with Mosaddek Hossain (50 not out) before the diminutive stumper walked off with an injury which he picked while taking a risky single in the previous over.
Thereafter, the Bangladeshi innings derailed as they lost the trio of skipper Mashrafe Mortaza (14), Taskin Ahmeda (2) and Mustafizur Rahman (0) in no time to be dismissed for 264.
Ferguson and all-rounder James Neesham were the main wicket-takers for the hosts with three scalps each while the seasoned Tim Southee chipped in with two wickets. Left-arm spinner Mitchell Santner also managed a wicket.
Brief Scores: New Zealand (Tom Latham 137, Colin Munro 87, Shakib Al Hasan 3/69) beat Bangladesh 264 (Shakib Al Hasan 59, Mosaddek Hossain 50 not out, Mushfiqur Rahim 42 retired hurt, James Neesham 3/36) by 77 runs.
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