Chris Tremlett and Graeme Swann bowled England to a remarkable innings victory after Sri Lanka were bowled out for 82 in the first Test in Cardiff.
A draw seemed likely after rain delayed the start of day five until 1400 GMT.
But England declared after two overs on 496-5, a first-innings lead of 96, as soon as Ian Bell reached his century.
Tremlett (4-40) grabbed two early wickets, before he and Swann (4-16) combined to tear through the tourists, with Stuart Broad finishing them off.
With the last eight wickets falling in just over an hour after the tea interval, it left England victorious by an innings and 14 runs.
It was an amazing end to a day's play that had begun with few supporters in the stands and even fewer expectations that the game would end in anything but a draw.
For the fourth day out of five, no play was possible during the morning as rain ensured the covers remained in place until four hours after the scheduled start time of 1100 BST, a period that appeared to have killed the game as a contest.
When the players did take to the pitch it was initially for only 12 balls - long enough for Bell to add five runs to his overnight score of 98 and reach his 13th Test century - before England's declaration brought them off again.
Because of the time eaten up by the weather, and with England's four-man bowling attack a man light following the side injury to James Anderson, the remaining 50 overs were expected to encapsulate a period of tame cricket during which England would give their fit bowlers practice time in the middle.
However, this does an injustice to the competitive nature and belief of this England side, who immediately seized the initiative in Sri Lanka's second innings and then steadily turned the screw on their increasingly demoralised and disorganised opponents.
The home side got off to a superb start thanks chiefly to towering opening bowler Tremlett, who claimed two quick wickets to stir England's interest.
In the second over he drew Tharanga Paranavitana into a wayward shot outside off and had him caught low at first slip by Strauss for 0.
In his next over, captain Tillakaratne Dilshan made a mess of a rising delivery and lobbed a catch back to the big bowler, with a review showing the ball had clipped his glove on its way through, leaving Sri Lanka 10-2.
After tea, home hope rapidly grew to genuine expectation as Tremlett and Swann tore into the tourists.
Tremlett claimed his third scalp from a superb, short of a length delivery that cut away from Mahela Jayawardene and caught the outside edge of the bat before nestling into the welcoming hands of Strauss at slip.
Then Swann got in on the act when Thilan Samaraweera played back and chopped onto his stumps to depart for a duck.
Panic had now set in for the tourists, whose middle order capitulated under the England onslaught.
In one Swann over, key man Kumar Sangakkara edged to Strauss at slip to depart for 14 and three balls later Farveez Maharoof needed a review to prove that he had indeed nicked one to keeper Matt Prior, to leave Sri Lanka 43-6.
It was 43-7 after the first ball of Tremlett's next over as England utilised the review system perfectly to overturn Billy Doctrove's initial summary that Prasanne Jayawardene had not gloved an attempted hook to Prior, to see the batsman off for just three.
Swann then dealt with Rangana Herath, who swiped across the line and was trapped lbw.
There followed the briefest period of minor resistance from Sri Lanka as Thisara Perera and Ajantha Mendis clung on, adding 30 between them.
But the introduction of Broad quickly resulted in the former prodding to short-leg where Bell was on hand to snatch a superb catch low down before last man Suranga Lakmal looped an easy catch to Alastair Cook from a short ball.
Brief scores
Sri Lanka 400 (P Jayawardene 112, Paranavitana 66, Anderson 3-66, Swann 3-78) and 82 (Swann 4-16, Tremlett 4-40)
England 496 for 5 dec (Trott 203, Cook 133, Bell 103*)
Results England won by an innings and 14 runs
MOM Jonathan Trott (England)
