Graeme Swann claimed 4-16 while Chris Tremlett picked up 4-40 as Sri Lanka were taken out piece by piece.
It was thought that the game was heading for a draw after rain hit most of the first few days, but the England bowlers stood up and took the game to Sri Lanka defeating the tourists by an innings and 14 runs.
"I don't think any of us thought it was hugely possible to get this result, but we knew we could have 50 overs to apply some pressure," said Strauss.
"There was some outstanding bowling from Chris Tremlett with the new ball, Stuart Broad as well, with Graeme Swann backing them up.
"We were on the receiving end of a similar result in Adelaide four years ago, and you can never relax in this game.
"We got some early wickets and then we went on."
