Spinner Mitchell Santner took the last two wickets on consecutive balls shortly before tea on the fourth day, the West Indies being dismissed for 203.
The result ensured a clean sweep, winning the series 2-0 after their innings and 67-run win at the Basin Reserve in the first test.
The West Indies had started the fourth day at 30 for two, requiring an improbable 444 to win.
They lost stand-in captain Kraigg Brathwaite in the sixth over of the day, caught at gully off Trent Boult.
That gave him his 200th test wicket, just the left arm bowler to reach that mark.
He is also the sixth New Zealand bowler to 200, after Richard Hadlee, Dan Vettori, Chris Martin, Chris Cairns and current team mate Tim Southee.
Shai Hope was struck on an arm by Neil Wagner and hooked the next ball straight to fine leg.
Sunil Ambris took a blow on his left wrist and after battling on a few minutes, retired hurt on five. A check revealed a broken bone and he is out of the ODI squad.
Wicketkeeper Shane Dowrich popped a catch to short leg but Roston Chase and Ray Reifer battled solidly to lunch and well into the second session, before they departed in quick order.
Chase completed his fifth half century, 64, while Reifer made 29 before falling to a fine low catch by captain Kane Williamson at gully.
Wagner finished with three for 42 and there were two wickets apiece for Southee, Boult and Santner.
The three-game ODI series starts in Whangarei next Wednesday, before which the tourists' have a one-day fixture against a New Zealand XI on Saturday.
The squad is significantly different from their test group, with the likes of batting heavyweights Chris Gayle and Marlon Samuels and Evin Lewis arriving this week.
The ODI series continues in Christchurch on December 23 and Boxing Day.
