After being dismissed for 101, Sri Lanka's batsmen showed more resistance in their second innings and by lunch had reached 58 for the loss of opener Dimuth Karunaratne. The tourists still trail by 339 runs.
Stuart Broad took three balls to claim his fourth wicket of the first innings when Suranga Lakmal edged behind without scoring.
Jimmy Anderson then tied things up when Lahiru Thirimanne (19) hoiked an ill-judged shot for Nick Compton to bag England's ninth catch of the innings.
When Sri Lanka batted again, Karunaratne batted diligently until edging a ball from Chris Woakes to Joe Root when he was on 26.
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At lunch Kaushal Silva was unbeaten on 23 and Kusal Mendis was on 8.
England are one up in the two-test series, having won the first test by an innings and 88 runs.
(Reporting by Neil Robinson; editing by Clare Fallon)
