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.
"In hindsight we should have batted first. We misread the wicket and once we saw it turning and bouncing the way it did there was a bit of concern."
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.
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.
New Zealand take the series 2-0 after the first Test in Dunedin was drawn and they won the second by an innings and 73 runs in Wellington.
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.
Rutherford, who was stuck at the spinner's end for a prolonged spell, offered a chance on 20 but Permaul did not see the ball early enough and it landed short of his grasp.
When he was on 24, Rutherford was given out caught behind, but the decision was overturned on appeal with the video replay showing the sound was the bat hitting the ground.
It was a remarkable change in the complexion of the match after the West Indies restricted New Zealand to 349 in their first innings, with the home side struggling to handle Narine on a turning wicket.
But the tourists suffered from questionable shot selection against the swing bowling of Boult and Southee in their second innings on Saturday, leaving New Zealand with a straightforward task.
"It looked like they had a plan for each and every batsman and the way their bowlers bowled on that wicket put us under a lot of pressure and we just did not have a response," captain Darren Sammy said.
"I'm most disappointed with our performance. We did not foresee what happened. We were thinking above 200 on the last day when we got spinning with the Narine factor it would be an interesting game."
Boult and Southee, along with the batting of Ross Taylor, laid the foundations for New Zealand's success.
Taylor, with 131 in the first innings, scored 495 in five innings in the series and he was only dismissed twice. From 10 Tests in the 2013 calendar year he averages 72.16.
Boult (four for 23) and Southee (3-12) destroyed the West Indies' second innings. Over the three Tests, Boult took 20 wickets at 15.40 and Southee claimed 18 scalps at 18.11.
The sides will now play five one-day internationals and two Twenty20 fixtures before India arrive in New Zealand next month for five one-day internationals and two Tests.