The tourists already had a difficult task ahead of them having scored just 134 in their first innings, with New Zealand declaring on 520-9 to take full control of the contest.
West Indies could only add a further 319 runs to their tally in their second innings as the hosts wrapped up victory by an innings and 69 runs with a day-and-a-half of the Test remaining.
The Windies' chase got off to a promising start with Kraigg Brathwaite (91), Kieran Powell (40), Shimron Hetmyer (66) and Shai Hope (37) all contributing respectable scores, but the latter's dismissal at 257-3 sparked another collapse.
West Indies began the fourth day 172 runs behind New Zealand, but they lost their final six wickets for just 46 runs to slump to defeat.
Matthew Henry was the pick of the bowlers for New Zealand with three wickets as the hosts wrapped up the victory less than an hour after lunch to give themselves a 1-0 lead in the series.