Mathews, meanwhile, also reached his half-century only to prove his critics that he is still the best batsman of the team. Kusal fell attempting one big stroke too many and swiping to Moeen, before catcher turned wicket taker, coaxing the ex-skipper into prodding ungracefully to Jos Buttler at midwicket.
The hosts were 98 for three at lunch, left needing a highly improbable world record chase of 462 or to bat for five more sessions for a draw.
But both fell after attacking shots, with Kaushal leg before trying to sweep Leach for 30 and Karunaratne caught and bowled by Ali for 26 and skipped down the pitch for an attempted heave.
Less than three overs later Karunaratne decided he would take the aerial route against Moeen, an ill-judged scheme that saw him club a firm return catch back at the off-spinner. One ball after Dhanajaya de Silva successfully overturned a caught behind decision Stokes tightened up his line and took an indisputable edge that nestled safely in the hands of Joe Root.More news: Trump erroneously accuses French President Emmanuel Macron of ‘very insulting’ comments
England's varied attack, which features three seamers and three spinners, probed persistently through the morning as captain Root employed attacking field placements.
England's players did a lap of honor to the appreciation of more than 6,000 of its fans at the game.
England had not won in 13 Tests, had never won in Galle and had had a miserable time in Bangladesh and India in similar conditions.
England took control of the series opener as they recovered from 103-5 on the opening day to post 342 all out, thanks largely to Ben Foakes' debut century, and then rolled Sri Lanka for 203.
Playing his 93rd and last test, Herath was the last man out, diving into his crease in a failed effort to avoid being run out. Suranga Lakmal led Sri Lanka during Chandimal's absences in Galle.More news: Giroud breaks goal duck in Chelsea win against BATE Borisov
"It will be touch and go for the second test match". When we used to play cricket, we learned from people who played with us, and we had like certain periods of game where we bowl short.
England's Ben Stokes, center, celebrates taking the wicket of Sri Lanka's Dhananjaya de Silva during the fourth day of the first test cricket match between Sri Lanka and England in Galle, Sri Lanka, Friday, Nov. 9, 2018.
Sri Lanka tried hard to force Rangana Herath's farewell Test into its final day but in vain.
Thisara Perera and Rangana Herath, who was playing his final worldwide fixture, took two wickets each.More news: Umesh, Bumrah, Kuldeep rested for final T20I against WI