Light rain was falling for much of the contest and 90 minutes were lost as the game was reduced to 18 overs a side, with the Black Caps ultimately completing just 15.
The West Indies made 132 for eight with Andre Fletcher registering a half-century but Tim Southee, Trent Boult and Corey Anderson took two wickets apiece to limit the home side.
Captain Brendon McCullum top-scored for New Zealand with 40 and despite Darren Sammy claiming three for 22, the Windies could not edge themselves ahead.
The tourists won the toss and decided to bowl and that looked a good decision as they removed big-hitting Lendl Simmons in just the second over.
Boult got one to swing in and, while the ball speared away towards the covers, it had hit the pad first and Simmons was gone for one.
Fellow opener Dwayne Smith (eight) was next to go off the last ball of the following over and he only had himself to blame as he heaved a Southee delivery from well outside off stump into the leg side and BJ Watling took a comfortable catch at deep mid-wicket.
Darren Bravo soon hit the first six of the game but then the rain came and the players were off for 90 minutes with the game reduced to 18 overs a side.
Bravo and Fletcher continued to clear the ropes as they put on 88 for the third wicket but the former fell for 30 when Anderson banged in a short ball and the top edge looped up to Luke Ronchi behind the stumps.
Fletcher brought up his 50 from 36 balls in the next over but was gone for 52 as he looped one up to Boult at third man to hand Ish Sodhi a wicket on his T20 international debut.
Sammy added just 10 before falling in similar fashion off Boult and Andre Russell had made just one when he skied one off Anderson into the hands of Ross Taylor.
Kieron Pollard (16) and Denesh Ramdin (one) then fell off the final two balls of the innings, with late wickets preventing the Windies from posting what would be considered a par score.
Jimmy Neesham hit a six and a four off consecutive balls in the second over of the reply but fell just two balls later to Krishmar Santokie.
The slingy paceman bowled a fuller ball and Neesham (11) inside-edged onto his off stump on the drive.
That brought McCullum to the crease and he went about upping the rate in typical fashion, smashing Santokie for a six and two fours in three balls.
Kane Williamson had not seen a great deal of the strike and had scored just 19 off 18 balls when a Sammy delivery looped up off the face off the bat and the tall skipper had to reach for a caught and bowled to leave New Zealand 65 for two.
Taylor hammered 18 off the 11th over as New Zealand moved to within touching distance but McCullum was gone for 40 when he did not quite get hold of a Sammy ball and Smith took the catch.
Anderson was next to fall for 15, miscuing a Sammy delivery high into the air for Sunil Narine, but the rain got stronger and New Zealand claimed the win on 117 for four with Taylor unbeaten on 28.
- Sports & Recreation
- Darren Sammy
- Corey Anderson
- Trent Boult
- Brendon McCullum
- Andre Fletcher
- New Zealand
- Tim Southee