The tourists reached 248-9 after losing the toss and being sent in to bat, a target the Black Caps overhauled with four overs remaining.
Opening batsmen George Worker and Colin Munro laid the foundation for the hosts' chase with a 108-run partnership.
New Zealand paceman Doug Bracewell was named Man of the Match after taking four for 55 with the ball, while spinner Todd Astle took three for 33 on debut.
The tourists struggled from the start of their innings, with dangerman Chris Gayle failing to fire and managing just 22.
Fellow opener Evin Lewis was the pick of the West Indies batsmen with a classy 76, while Rovman Powell staged a stirring rearguard action to score 59 off 50 balls.
However, New Zealand always looked comfortable pursuing the relatively modest total.
The loss leaves the West Indies yet to register a win on their New Zealand tour after a 2-0 whitewash in the Test series.
They have not won an ODI series in New Zealand since 1995, and are in a form slump that has seen them win only three of 17 ODIs contested in 2017.
The next fixture in the three-match ODI series is in Christchurch on Saturday.
New Zealand captain Kane Williamson and paceman Tim Southee will be rested for the second and third ODIs.
chris gayledough bracewellevin lewisJason HolderKane WilliamsonNew Zealand vs West IndiesNew Zealand vs West Indies 2017Tim Southee
First Published: December 20, 2017, 12:41 PM IST