The home side, needing just 122 runs to seal the series 2-0, reached their target for the loss of two wickets after the West Indies collapsed in the face of hostile New Zealand swing bowling.
The rapid end to the match surprised New Zealand captain Brendon McCullum after his side trailed by 18 runs on the first innings following a mesmerising spell of spin bowling by Sunil Narine.
"I certainly didn't expect it to end up as quickly as this," McCullum said, admitting he probably made the wrong decision to bowl first.
But once New Zealand seamers Trent Boult and Tim Southee tore through the West Indies' second innings, scuttling the tourists for a paltry 103, it became easy work for New Zealand to bat out the win.
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Hamish Rutherford, who sealed victory with a boundary to take New Zealand to 124-2, finished on 48 not out, with Ross Taylor on two.
Peter Fulton was the first wicket to fall on Sunday, caught and bowled by Darren Sammy for 10, and Kane Williamson was dismissed for 56, bowled by Veerasammy Permaul.
It is the first time New Zealand have achieved back-to-back Test victories against a top-eight side since March 2006 -- also against the West Indies. The Black Caps also won that three-Test series 2-0.
New Zealand resumed their second innings on the fourth morning at 6-0 and although Narine, who took six wickets in the home side's first innings, bowled unchanged throughout the first session, he went without reward.