Stuart Broad's side were set a target of 169 runs to ensure that they progressed through to the semi-finals stage of the competition along with Sri Lanka, and at the expense of fellow group members West Indies.
Bairstow's dismissal brought Samit Patel to the crease and the all-rounder was the only England batsman who provided some real resistance to Sri Lanka's bowling attack.
Patel, who made 67 runs before he was bowled by Malinga, eventually ran out of partners though as the likes of Eoin Morgan (10), Ravi Bopara (1), Jos Buttler (8) and skipper Broad (1) all went cheaply.
Graeme Swann produced a fight-back of sorts with a knock of 34 from just 20 deliveries, but his efforts could not reverse England's fortunes.
England lost three of their five matches during the competition.