Victory at the National Cricket Stadium was revenge for Ireland after the West Indies completed a 3-0 whitewash in the one-day series on Sunday.
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They reached 7-208 after winning the toss and electing to bat, setting a T20I world record for highest score in a powerplay with 0-93 in the first six overs.
Opener Paul Stirling hit 95 off 47 balls, including eight sixes, while Kevin O'Brien made 48 before being bowled by Bravo.
O'Brien's dismissal sparked a mini-collapse of four wickets for 10 runs, with Ireland recovering from 4-164 to post a winning total.
West Indies fall agonisingly short
Chasing 209 to win, the hosts needed 13 off the final over on Wednesday but lost Sherfane Rutherford and Dwayne Bravo.
Bravo, recently recalled to the T20 squad, had earlier hit a six off the second ball of the over to give the West Indies hope.
But he was caught by Gareth Delany off Josh Little with one ball remaining and the hosts could reach only 7-204.
Evin Lewis top-scored for the Windies with 53 and Kieron Pollard hit 31 while Little claimed three for 29 for Ireland.
Ireland’s stunning win captured the attention of the cricket world, especially considering West Indies are the reigning T20 world champions.
My God. I just checked score. What an incredible batting so far. #WIvIRE— Dev :) 🇮🇳 (@noddy1212) January 15, 2020
WOW! @Irelandcricket have just set a new T20 international record for a power play.— Test Match Special (@bbctms) January 15, 2020
93 from 6 overs with @stirlo90 reaching a 50 from 20 balls.
FOLLOW👇https://t.co/kvHbeCGS1f#bbccricket #WIvIRE pic.twitter.com/xatDgSSWIo
Three months after losing to Canada (the world no 23), Ireland beat the world champions West Indies in a T20 away.— Tim (@timwig) January 15, 2020
Safe to say that is a huge day out for @Irelandcricket and their players. Beating the world champs in their back yard. Special mention to Josh Little , Craig Young and George Dockrell (3catches and his last over swung it). Series up and running well done Captain @balbo90— Niall John O Brien (@niallnobiobrien) January 15, 2020
There is a small band of dedicated Irish supporters here in Grenada delighted for them. We may party tonight #wivire remember ireland just beat the T20 World Cup winners in their own back yard. St kitts hosts last two games sat and sun— john kenny (@JohnKennyMedia) January 15, 2020
Stirling and KOB are unstoppable today!— Haider Azhar (@HaiderAzhar) January 15, 2020