The Black Caps initially made heavy weather at the start of the run-chase as they slipped to 32-3 in the 11th over but Tom Latham and Mark Chapman put together a partnership of 38.
Latham however fell for 10 to leave the hosts on 70-4 before Chapman was joined in the middle by Michael Bracewell.
The duo added a match-winning stand of 70 for the fifth wicket thattook the game away from the Caribbean outfit.
Chapman was eventually dismissed for 64 off 63 balls but Bracewell was unbeaten on 40 to see the Kiwis over the line in the 31st over.
Matt Henry had earlier returned figures of 4-43 in 9.2 overs as West Indies were bowled out for a below-par 161 in 36.2 overs.
Roston Chase struck a valiant 38 but did get the necessary support from his fellow batters to make a game of it.
The ODI series victory follows New Zealand's 3-1 win in the five T20Is with both teams now preparing for the three Test matches that starts on 2 December.
Justin Greaves says he will saviour a 'special day' after scoring a maiden double-century to help West Indies to an epic draw in the first Test against New Zealand in Christchurch.
New Zealand legend Kane Williamson has announced his retirement from T20 International cricket with immediate effect to focus on the other two formats of the game.
England's batting frailties came to the fore once again as New Zealand completed a 3-0 series whitewash with a tense two-wicket win in Wellington on Saturday.
England secured an eight-wicket win over New Zealand in Visakhapatnam to finish the Women's World Cup group stage in second place.
