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Kusal Mendis added 46 runs with Mathews for the fourth wicket, but he too could not convert a good start into a big innings and fell for 45.
Moeen Ali grabbed four wickets, while Jack Leach took three wickets.
"I'm very happy with the way Mathews conducted himself throughout the game, and his commitment for running between the wickets and for the batting", he said.
While the side did not have the best of warm-up games, England's recent record in the 20-over format has been encouraging, with most of the players coming on the back of the their domestic T20 tournament Women's Super League.
"We're really proud of him and really proud of the rest of the guys".
Overnight batsmen Dimuth Karunaratne and Kaushal Silva saw through the first hour without any damage even if they had a little luck when Karunaratne, on 16, edged Moeen Ali but Ben Stokes grassed the easy catch at slip. The ball earlier he was given out but reprieved on review.More news: Adriana Lima’s Tearful Final Walk as a Victoria’s Secret Angel
He had earlier appeared confident at the crease, employing the sweep shot especially well against all England´s spinners, while secure in defence.
Home skipper Dinesh Chandimal is unable to bat any higher than number seven because of a groin injury that kept him off the field for all of Thursday, weakening Sri Lanka's batting order.
The final session began badly for the hosts. In the first innings, for example, Niroshan Dickwella pushed at a Moeen Ali delivery, and put it straight in the hands of the short cover that had been placed there for exactly that stroke.
Soon afterwards Angelo Mathews, dropped on 18 by James Anderson, went for 53, was caught by Jos Buttler at midwicket with Ali the wicker-taker again.
The remainder of the innings was a procession against a tired fielding unit, Jennings adding his next 46 runs at a relative canter alongside Jos Buttler (35) and Foakes (37).
England's varied attack, with three quicks and three spinners, applied substantial pressure, with the slightly expensive Adil Rashid the only disappointment so far.
"Very proud, I thought the way we played throughout the four days is excellent", England captain Joe Root said, singling out Ben Foakes, whose century on debut earned him the man-of-the-match award, for special praise. "Yes, it´s a dream come true to be fair", said the Surrey wicketkeeper-batsman, brought in to replace the injured Jonny Bairstow.