The hosts were restricted to 116 for eight, Chris Gayle top-scoring with just 18 as Tim Murtagh, Kevin O’Brien and Alex Cusack took two wickets apiece. From eight for two, Ireland powered to 117 for four to win with five balls to spare as Ed Joyce top-scored with 40 not out.
Windies captain Darren Sammy won the toss but his side struggled to build momentum, save for two early sixes from Dwayne Smith (14).
He and Gayle put on 31 before falling in successive overs and wickets continued to fall at regluar intervals.
Marlon Samuels and Lendl Simmons made 16 apiece and Andre Russell hit 15, with the 10 batsmen required all scoring between three not out and 18.
Cusack was the pick of the bowlers with two for 17 in four overs, figures matched by O’Brien in two while Murtagh took two for 28. Irish captain William Porterfield hit the third ball of their innings for four but was dismissed by the next and opening partner Paul Stirling followed in the next over.
But Joyce put on a steady 29 with Gary Wilson before the crucial partnership, 58 with Andrew Poynter.
Poynter hit six fours in an innings of 32 from 30 balls before being bowled by Sunil Narine.
Ireland still needed 22 at that stage but Joyce, whose watchful 49-ball innings contained just two boundaries, was joined by O’Brien (15no) to see them home.
The teams meet again over 20 overs on Friday before a one-off one-day international on Sunday, also at the Jamaican venue.