Chasing a fighting 138-run target, Sri Lanka were bundled out for 101 runs in 18.4 overs in front of 35,000 dazed fans.
It was the West Indies’ first major title since 2004 when they lifted the Champions Trophy in England.
West Indies bowlers were on a roll as they dented Sri Lankan chase by removing seven batsmen within 70 runs in 15 overs in the final clash of the World T20.
Chasing 138, Sri Lanka lost Tillakaratne Dilshan, for a duck, in the second over.
Though Jayawardene and Sangakkara steadied the innings with a brisk stand, West Indies fought back to derail hosts’ chase with quick wickets.
Samuel Badree gave West Indies crucial breakthrough by dismissing Kumar Sangakkara after 42-run stand for the second wicket.
Sangakkara’s dismissal came just before Sri Lanka crossed 50-run mark.
At the score of 51 Darren Sammy bowled out Mathews in the 11 th over.
Earlier, Ravi Rampaul struck in the second over to dismiss Tillakaratne Dilshan for a duck, spoiling Sri Lanka start in the chase of a modest 138 in the final.
Rampaul bowled out Dilshan after West Indies fought their way to 137/6 in 20 overs.
Sri Lanka’s unorthodox spinner Ajantha Mendis grabbed four wickets for 12 runs to restrict the West Indies to a modest total.
A sell-out crowd of 35,000 at the Premadasa stadium cheered every dismissal as the West Indies, electing to bat, fell apart once Chris Gayle was removed in the sixth over for only three runs.
Marlon Samuels was the only batsman to defy the spot-on Sri Lankan bowling, making 78 off 56 balls with the help of six sixes and three boundaries.
His brilliant strokeplay helped the West Indies add 105 runs in the last 10 overs after they were reduced to 32-2 from the first 10.
Sri Lanka took an early grip on the match by keeping the West Indies down to 14-2 in the first six powerplay overs after Johnson Charles had been dismissed off the fifth ball of the match.
The West Indies had to wait till the 19th delivery to score their first run with the bat and Gayle needed nine balls to get off the mark.
The left-hander struggled for 16 deliveries to make three before he was trapped leg-before by Mendis in the sixth over.
It was not till the 12th over that the West Indies, who pummelled Australia in the semi-finals, showed the first signs of aggression as Dwayne Bravo pulled 19-year-old spinner Akila Dananjaya for a six over mid-wicket.
Samuels responded by smashing three sixes in the next over of sling-arm fast bowler Lasith Malinga, two of them in succession over mid-wicket and extra-cover.
Bravo helped Samuels add 59 runs for the third wicket when he was given out leg-before by Australian umpire Simon Taufel, even though replays showed the ball go off the bat on to the pad.
Mendis then dismissed the dangerous Kieron Pollard and Andre Russell off successive deliveries in the 16th over, but West Indies captain Darren Sammy denied the spinner a hat-trick.
The 17th over, bowled by Malinga, produced 19 runs as Samuels smashed a boundary and two consecutive sixes to leave the frontline bowler with unflattering figures of 0-54 from his four overs.