Ireland: 307-6 (45.5 overs) Stirling 92, Joyce 84, Taylor 3-65
West Indies: 304-7 (50 overs) Simmons 102, Dockrell 3-50
Ireland won by four wickets
Ireland added West Indies to their list of World Cup scalps with a four-wicket win in their opening match in Nelson.
Lendl Simmons (102) shared 154 with Darren Sammy as the Windies recovered from 87-5 to post 304-7.
But Ireland openers Will Porterfield and Paul Stirling put on 71 and Stirling (92) added 106 with Ed Joyce.
Joyce hit 10 fours and two sixes in 84 and Niall O'Brien 79 not out as Ireland won with 25 balls left, their fourth World Cup triumph over a Test nation.
It is the fifth successful World Cup chase in excess of 300 and three of them have been by Ireland.
Having beaten Pakistan in their first World Cup in 2007 and England in the 2011 tournament, Ireland were almost considered favourites from the outset at the picturesque New Zealand venue.
The Windies, winners of the first two World Cups in the 1970s, are eighth in the ODI rankings, were skittled out for 122 by England in a warm-up match and are rumoured to be in disharmony following the omission of Kieron Pollard and Dwayne Bravo from their squad.
Some intrepid fielding and accurate seam bowling from Ireland after choosing to field quickly led to two wickets falling in the eighth over.
Big hitting Gayle and Marlon Samuels both launched towering straight sixes before both were dismissed by 22-year-old George Dockrell in the 22nd over, the left-arm spinner with figures of 3-23 at one point.
"I'd say this is a better victory than the one against England, that was a one-man show from Kevin O'Brien, this was a team effort, five or six people putting their hands up and delivering a world class performance."
Sammy unleashed some innovative strokes, often with ferocious power, in a thrilling partnership with Simmons, who accelerated stylishly as West Indies became the fifth successive team in the tournament to post in excess of 300 when batting first.
But far from overawed, the Irish openers punished some loose bowling in a fluent 13 over stand.
Man-of-the match Stirling hit three sixes in his pugnacious innings and was within eight of his sixth ODI hundred when, suffering from severe cramp, he edged behind in the 28th over with 128 still needed.
With the Windies looking ragged and forlorn, Joyce effortlessly guided the Irish within 32 of the target and despite three wickets in 17 balls, John Mooney, just as he did against England four years ago, struck the winning runs.
Ireland, coached by former West Indies batsman Phil Simmons, uncle of Lendl, next face the UAE in Pool B on 25 February.