Captain Mathews took four wickets in England's second innings before making an vitally important 160 to but the game beyond the reach of the hosts, and the all-rounder could not hide his delight after the match as Sri Lanka proved that they were capable of succeeding outside of subcontinent conditions.
"It means everything to be honest," he told Sky Sports News. "We played some really good cricket.
"We play a lot of cricket in the subcontinent and people don't expect us to come over and win in England and we proved that today."
Since taking over the Test captaincy in February 2013, Mathews has scored 946 runs at an average of 78, which is the second-best record of anyone who has skippered their country five or more times.