Sonal Dinusha's maiden Test hundred kept Sri Lanka afloat, but India remained firmly in command after day three of the opening Test between the neighbours in Galle on Monday.
Replying to India's 462, Sri Lanka were bowled out for 284 despite a spirited sixth-wicket partnership of 146 between Dinusha (100) and Niroshan Dickwella (80).
India could not add to their first-innings lead of 178 as dark clouds and the possibility of a storm prompted an early end to the day three action.
Earlier, Sri Lanka needed only four balls to take India's final first-innings wicket, but soon found themselves in deep trouble after losing half their own side during the morning session.
Mohammed Siraj opened the floodgates by dismissing Nishan Fernando for a second-ball duck before India's three-pronged spin attack took control.
Left-arm spinner Manav Suthar (4-76) struck with his first delivery as Dinesh Chandimal (4) edged behind. Lahiru Udara (27) struck six fours before slicing Suthar to backward point.
Shubman Gill then produced a stunning diving catch at extra cover, leaping to his left to send back Kamindu Mendis (14) off Kuldeep Yadav.
The collapse became a full-blown crisis when Ravindra Jadeja had Sri Lanka captain Dhananjaya de Silva caught at slip for 21, leaving the hosts reeling at 90-5.
Dickwella and Dinusha, however, mounted a defiant fightback that frustrated India through the afternoon.
Playing his first Test in three years, Dickwella was given a reprieve on 20 when KL Rahul dropped him at slip. He made India pay, combining with Dinusha to deny the visitors a wicket throughout the second session.
Dickwella eventually fell caught behind off Prasidh Krishna, but Dinusha could not be denied his hundred, which he brought up with a single off Suthar.
His splendid innings, featuring four fours and two sixes, ended when Jadeja (3-57) trapped him lbw.
Dinusha, convinced he had got an inside edge, immediately reviewed the decision. But UltraEdge showed no contact, and he walked off shaking his head after a stellar innings.