The 24-year-old took 5-28 as the Kiwis were bowled out for 221 in reply to the West Indies 241 all out and gave the hosts a 4-1 win in the series.
The New Zealanders - who left out experienced all rounder Jacob Oram and were already without several experienced players who have been struck down with injury - saw several of their top order make a decent start before failing to move beyond 40.
The only one to do so was Kane Williamson as the 21-year-old threatened to take them to victory with an impressive 69 and it took a superb catch by Gayle at mid wicket, off the bowling off Narine, to dismiss him.
The West Indies had been teetering on 37-3 before a 60 run partnership between Marlon Samuels and Dwayne Bravo steadied the ship.
Samuels fell when on 43, caught by Martin Guptill off Tim Southee, but Bravo played an unaccustomed patient innings to make his slowest ever half century before he fell for 53, caught by Brendon McCullum off Andrew Ellis.
The hosts faltered again only for Andre Russell to come to their rescue batting at nine as he rattled off a stunning 59 not out to at least give his side a reasonable target to defend.
Veteran New Zealand bowler Kyle Mills had something to celebrate as having become New Zealand's joint second highest wicket taker in this form of cricket when he had Chris Gayle caught for just five, he moved into second on his own with a further two in the innings.
Mumbai Roundup: 9 incidents that took place this week
Photos: Ajay Devgn, Parineeti, Tabu at 'Golmaal Again' trailer launch
Photos: Dipika Pallikal Karthik oozes oomph in bikinis and sarees
Photos: Kareena Kapoor Khan's grand birthday bash
Photos: 'Dangal' girls Sanya Malhotra, Fatima Sana Shaikh's dinner outing