A rain-affected match appeared destined for a draw after England declared their first innings on 496 for five -- a lead of just 96 -- with only 51 overs left on Monday's fifth and final day here at Sophia Gardens.
But what had seemed a moribund match was sparked into life by England fast bowler Chris Tremlett who, maintaining an accurate line and length at sharp pace ripped through the top order on his way to four for 40.
Off-spinner Graeme Swann (four for 16) followed up and Sri Lanka were bowled out inside 25 overs to go 1-0 down in this three-match series.
They do not have long to regroup before the second Test at Lord's on Friday and Dilshan said: "I am really calm, I can't be angry. "It will be difficult to forget this Test match but we have to stick together as a team.
"We can regroup and come back for the Lord's Test in a positive mind and then we can play some good cricket there.
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This was Sri Lanka's first Test outside the subcontinent since 2008 and this defeat, coming