Darren Sammy's men produced a superb performance with the ball to restrict Sri Lanka to 122 for nine. Only Thisara Perera, who hit 40 off 29 balls, offered any resistance.
It's a 2nd victory for West Indies, who beat England by six wickets on Wednesday, and they will qualify for the last four if they beat South Africa.
Defending champions Sri Lanka face a battle to advance, and their match against England in Delhi now looms large, with the loser likely to be eliminated.
