The hosts in Roseau put on 132-8 in 18 overs after New Zealand skipper Brendon McCullum sent them in to bat.
And the Black Caps were on target to complete the chase at 117-4 through 15 overs, before rain - which had been present for much of the contest - finally forced the players from the field, resulting in a 12-run Duckworth-Lewis method victory to the tourists.
Andre Fletcher starred for the Windies in the absence of Chris Gayle, making 52 off 39 balls including one four and four sixes.
Fletcher and Darren Bravo (30 off 28) put on 88 for the third wicket after Windies openers Dwayne Smith (eight) and Lendl Simmons (one) departed early to leave the home side at 10-2.
Kieron Pollard (16) and captain Darren Sammy (10) chipped in with late cameos to boost the total, although it would not be enough.
McCullum anchored the Black Caps' chase with 40 off 35 including four boundaries, while Ross Taylor's unbeaten 28 off 20 guided the tourists home.
Corey Anderson threatened to tear apart the Windies attack as he did so on New Year's Day when he scored the fastest-ever one-day international century, but he was Sammy's third scalp of the inning as he holed out for 15 off nine balls.
The Windies must improve their record against NZ in T20s - they have won two of just nine against them - when the second T20 begins on Sunday.