Following victories in Galle and Kandy, Joe Root’s side have two full days to finish off their beleaguered hosts who will resume on 52 for four chasing a ground record 327.
Jos Buttler became the latest member of the touring team to weigh in with a crucial contribution, arriving at the crease on 39 for four and playing against type for a mature 64 - his best knock of the series - to usher England to a healthy 230 all out.
Buttler’s 89-run stand with Ben Stokes (42) was the turning point of an innings that had threatened to enter tailspin, with Lakshan Sandakan playing the role of enabler with two grievous self-inflicted wounds. The left-arm wrist-spinner twice had Stokes caught - at cover on 22, at slip on 32 - only for replays to show he had overstepped the no-ball line on each occasion.
England were afforded 17 overs to make inroads into Sri Lanka’s batting lineup and rammed home their advantage with zeal. Moeen Ali, on new-ball duty, accounted for both openers as Danushka Gunathilaka nicked a sharp off-break to slip and Dimuth Karunaratne exposed his off stump with a loose shot.
Jack Leach had Dhananjaya De Silva lbw on a smart review and Stokes landed one more before stumps, goading Angelo Mathews into a brainless pull to midwicket.
England began the day 99 ahead but quickly managed to turn a hard-won position of strength into a flimsy top-order procession.
Keaton Jennings succumbed lbw to the first ball of the day, Dilruwan Perera coaxing a wicket-to-wicket delivery into the front pad, before picking off Rory Burns in identikit fashion.
The duo have had moments of success in the first series of the post-Alastair Cook era but ended on a low here and will look forward to resuming their union away from the exaggerated spin of Sri Lanka.
Perera’s probing saw him pick up first-innings centurion Jonny Bairstow next, with Kaushal Silva on hand to hold a firm chance at short-leg, and when Root fed a leading edge back to Malinda Pushpakumara just nine balls later England were wobbling badly.
Stokes and Buttler combined to nudge the scales back in the opposite direction, adding 71 before lunch and 18 more afterwards. There was much to be impressed by in their work, with big swings of the bat shelved for more conservative strokes and Buttler consistently leaving his crease to knock the bowlers off their lengths. When that ploy worked best they cashed in, milking 20 runs from two ragged Sandakan overs.
Yet their stand still hinged on several instances of good fortune, Sandakan’s wandering front foot giving a disbelieving Stokes second and third lives. Buttler was much more controlled but still had to overturn a tight lbw verdict, rapping the knee roll in front of middle but apparently skipping over.
He might also have fallen to the first ball after lunch, when a thin edge down leg side failed to stick in Niroshan Dickwella’s gloves. Stokes’ luck eventually expired when he failed to clear long-on off the probing Perera but Buttler continued to nudge, push and steer his way to a busy half-century.
Buttler’s willingness to advance eventually cost him, stumped as Sandakan dragged one down leg, but it had also enabled him to find consistent scoring shots throughout his innings despite just three boundaries.
Buttler’s departure left England 264 ahead with four more wickets and Sri Lanka eyeing a swift clean up job. Stuart Broad obliged by lasting just five balls but the resistance continued elsewhere, Moeen and Adil Rashid adding 22 and 24 respectively - valuable lower-order runs at the business end of a match.
Ben Foakes ended unbeaten on 36 not out, bringing his average to 69.25 in a standout maiden series, with three referrals all going against the hosts before Leach’s nick completed Perera’s five-for.