Angelo Mathews was 79 not out as Sri Lanka reached lunch on 7-311 with a healthy lead of 203 runs over England on day four of the second Test at Headingley.
With the tourists resuming on 4-214, Mahela Jayawardene added 24 to his total before edging a James Anderson delivery behind to Matt Prior for 79.
Liam Plunkett then struck twice in as many balls. Dinesh Chandimal (7) was caught at deep square leg by Gary Ballance before Dhammika Prasad (0) was caught by Joe Root coming in from third man.
Plunkett was on his hat-trick for the second time in as many innings, but captain Mathews denied him by pulling a short ball for a single.
Rangana Herath is with Mathews at the crease, on seven.