The return of Chris Gayle could not spark the West Indies, with the short-form master managing only 22 as his team struggled to 248-9 after losing the toss and being sent in to bat.
The Black Caps always looked comfortable chasing the modest total, overhauling it with four overs remaining at Whangarei's Cobham Oval.
West Indies skipper Jason Holder said his side needed to be "a lot better with the bat" as they chase their first ODI series win in New Zealand since 1995.
"It was tough, I didn't think we had enough runs," he said. "We kept losing wickets at crucial stages of the game and never really gathered momentum.
"That obviously hampered us today and we've just got to correct it."
There were some bright spots for the Windies, with opener Evin Lewis notching a classy 76 and Rovman Powell staging a pugnacious rearguard action to score 59 off 50 balls.
Gayle -- fresh from notching a record 18 sixes in the Bangladesh Premier League T20 final -- had an uncharacteristically subdued innings.
He fell victim to resurgent New Zealand paceman Doug Bracewell, who was named man of the match after celebrating the end of a 15-month exile from the national team by claiming four wickets for 55.
Bracewell had fallen out of favour with New Zealand Cricket after a string of off-field incidents, including a drink-driving conviction earlier this year.
The 27-year-old was called up as a last-minute replacement for Colin de Grandhomme after the all-rounder ruled himself out of the series following his father's death.
"For him to come back and perform the way he did, taking some big scalps for us, was outstanding," said captain Kane Williamson.
Spinner Todd Astle also contributed three for 33 in his ODI debut as the Black Caps attack maintained constant pressure with the ball.
New Zealand opening batsmen George Worker and Colin Munro laid the foundation for the hosts' chase with a 108-run partnership.
Worker finished on 57 and Munro 49 as New Zealand's top order all made starts, with Williamson contributing 38 and Ross Taylor unbeaten on 49.
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 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.
Williamson and paceman Tim Southee will be rested for the second and third matches.
First Published: December 20, 2017, 2:33 PM IST