Chasing a meagre 56 runs for victory on day three, Kane Williamson and Devon Conway cruised to the total after Tom Latham went for nine.
The Kiwis needed just 60 balls to take a 1-0 lead in the series with one game to play.
Disaster struck early for the Windies, a mix up between Kavem Hodge and Brandon King saw the latter run out by sub fielder Michael Bracewell.
In the same Michael Rae over, Shai Hope would find the boundary from his first ball faced, only to chip one straight back to Rae three balls later in an eventful six deliveries to put the West Indies in serious strife, still trailing the home side.
Skipper Roston Chase followed soon after for just two, edging a Jacob Duffy delivery behind, leaving the West Indies three runs behind and five wickets down.
Hodge was next to go, caught by another sub fielder in Will Young from the bowling of Zak Foulks.
Duffy and Rae made quick work of the tail, the visitors losing their last four for only 15 runs as they capitulated to 128 all out, Duffy picking up a second career five wicket haul.
The third test in Mt Maunganui starts next Thursday.
