Half-centuries from openers Dwayne Smith and Kieran Powell saw the West Indies beat Ireland by four wickets in Sunday's one-day international at Sabina Park in Kingston.
Ireland, who fell just short of beating the West Indies in the second Twenty20 international between the nations earlier this week, reached 202 all out with Gary Wilson scoring 62 runs off 96 balls.
The hosts chased victory without loss until the 17th over, which saw Smith become one of Thompson's two victims - he also did for Darren Bravo - after he had smashed 55 runs off only 53 deliveries including five fours and three sixes.
Edwards reached 57 before falling to Paul Stirling, leaving Dwayne Bravo and Marlon Samuels to shepherd the West Indies to victory, the latter smashing a huge six over long-off to end the match with 13 overs remaining.
The series victory over Ireland will give the West Indies a confidence boost with the first of three ODIs against England set to take place in Antigua on Friday.