After bowling out the tourists for 232, the Blackcaps easily reached their target with eight wickets in hand.
Martin Guptill starred for the hosts, smashing an unbeaten 117.
The second match will be played at Christchurch on Saturday.
New Zealand win first ODI against Bangladesh
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On Virgin Radio today
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TiestoMidnight - 1:00am
Tiesto's Club Life is the perfect show to keep your Saturday night buzzing all the way into Sunday.
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Ultra Music Festival
1:00am - 3:00am
Hit Music
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New Religion
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The Other Side
Jason Derulo