Narine took four for 12, including two wickets with consecutive deliveries, to turn the game in the Windies' favour and leave New Zealand's hopes of chasing down 178 in tatters.
Chris Gayle had earlier hammered 53 while a late blast from Dwayne Bravo (35 not out) pushed West Indies' total up to 177 for five, which proved more than enough after New Zealand were all out for 116 in the 19th over. Gayle was man of the match in the opener after making an unbeaten 85 and was just as destructive on Sunday after a cautious start.
The Windies did get off to a flyer after winning the toss but it was not Gayle who initially came to the fore. Kyle Mills conceded 14 off his first over, with Dwayne Smith striking two sixes in three balls. The opener was dismissed in the next over when he skied a return catch to Doug Bracewell, who then saw his next two deliveries hammered for successive fours by Johnson Charles.
At the other end, Gayle saw out a maiden off Mills' second over before exploding into action in the eighth over, hammering Bracewell for a six and a four. Just as it looked like the Windies were starting to control proceedings, Charles departed for 36 after paddling a short Rob Nicol ball to Tim Southee at fine-leg.
Gayle continued unabashed, thumping two successive sixes and a four off the under-fire Bracewell to bring up his half-century. The left-hander did not last much longer and was bowled by Nathan McCullum, who also had Lendl Simmons caught at backward square-leg for 18 four balls later.
Bravo hammered his first ball for six over long-off and clubbed another three maximums and a four to take his score to 35 not out off just 11 balls.
Martin Guptill helped the Black Caps make a promising start, striking two fours and a six but he holed out to Fidel Edwards at deep cover to give Narine his first success. Fellow opener Nicol perished off the next ball, stumped after being dragged out of his crease, and New Zealand's challenge never recovered.
Kane Williamson and Southee departed cheaply before Dean Brownlie was bowled by Narine attempting to push through the covers. Daniel Flynn (22) struck two sixes in a rare highlight for Williamson's side but he miscued to Gayle at point off Marlon Samuels, who then bowled Tom Latham in his next over.
Narine had his fourth wicket when Andrew Ellis skied high down the ground and was caught by Bravo, who took the final two wickets to seal an emphatic victory for the Windies.