England openers Sam Robson (10), who fell for one on debut in the first innings, and Alastair Cook (15) made it through to lunch unscathed at as they added a further 27 runs to their lead with five sessions left to play on a lifeless surface.
If England, playing their first test since coach Andy Flower was replaced by Peter Moores, entertained hope of forcing a result ahead of the second and final test in Headingley next week, they needed to finish off the tail quickly but initially persisted with a negative field.
They did not introduce a close catcher behind the wicket until the attack-minded Mathews had flashed consecutive boundaries through the gap between wicketkeeper Matt Prior and Chris Jordan at fourth slip.
There also appeared to be a plan to bowl short at tail-ender Rangana Herath (2), the futility of which became apparent when James Anderson hit his middle stump with the first full-pitched ball he sent down.
Mathews, who along with fellow century-maker Kumar Sangakkara (147) helped Sri Lanka pass the follow-on target in Saturday's evening session, brought up a well-deserved 100 when he smashed an Anderson full toss through extra cover, having raised the milestone off 171 balls.
He was unable to push on, however, falling lbw to Liam Plunkett for 102 from the next ball he faced, good reward for the England paceman, playing his first test in seven years, who bowled with impressive speed.
Chris Jordan, on debut, wrapped up the innings in rare fashion when Nuwan Pradeep (4) was struck on the shoulder by a bouncer and subsequently hit the wickets with his bat as he fell to the ground, his side having added 38 runs to their overnight score in a little more than an hour.
(Editing by John O'Brien)
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