England needed to chase the 170-run target in less than 13 overs to qualify for the semifinals but paceman Malinga's performance (5/31) made it a lop-sided affair.
England ended 150 for nine through a fighting 67-run knock from Samit Patel and and his 51-run stand for the eighth wicket with Greame Swann (34).
Sri Lanka's win pushed England out of the tournament since they had just one win from three Super Eight matches in Group I while the Caribbean side had two.
The West Indies had edged past New Zealand in a thrilling match early in the day to keep themselves in the hunt.
None of the Sri Lanka batsmen played a big knock but they rode on a collective batting effort to reach a competitive 169 for six.
Mahela Jayawardene (42), Angelo Mathews (28) and Jeevan Mendis (18) got good starts but could not convert those into big innings after the hosts were sent in to bat.
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Thisra Perera (25 not out) and Lahiru Thirimanne (13) blasted some big shots towards the end to lift the side to a fighting total.
But Malinga's sensational over -- third of the innings -- in which he scalped Luke Wright (13), Jonny Bairstow (2) and Alex Hales (3), took it away from them.
England were reeling at 18 for three in three overs and never recovered from that shock start.
Malinga added wickets of Jos Butler and Patel later in the innings while spinner Akila Dananjaya contributed in the win of his side by dismissing Eoin Morgan (10) and Broad (1).
Broad (3/32) and Swann (2/26) did well for England in the second half of the Lankan innings as both of them got wickets in successive balls to keep the side in hunt.
Interestingly, Kumar Sangakkara led Sri Lanka today in place of regular skipper Jayawardene.