India's bowlers took five wickets in the first session on day three of the opening test to reduce Sri Lanka to 99-5 at lunch in Galle on Monday.
Sri Lanka trail by 363 runs with five wickets in hand, with Sonal Dinusha on 14 and Niroshan Dickwella eight.
After posting 462 all out, India's attack rammed home the advantage with some disciplined bowling on a pitch offering plenty of assistance to the spin bowlers.
Mohammed Siraj struck early, in the second ball of the innings, when he had Nishan Fernando caught at slips before the spin bowlers came into the equation.
Left-arm orthodox spinner Manav Suthar, playing just his second test match, struck in his first ball by claiming the wicket of Sri Lanka's most experienced batter Dinesh Chandimal.
There was turn and bounce for Suthar and Chandimal, trying to defend, edged one to wicketkeeper Rishabh Pant for four.
Bounce again from Suthar proved to be the undoing of Lahiru Udara, who hit the ball straight to backward point. He made 27.
Sri Lanka slumped to 59-4 when Kamindu Mendis was superbly caught at covers by a diving Shubman Gill as left-arm wrist spinner Kuldeep Yadav struck.
With five minutes to go before lunch, Ravindra Jadeja removed captain Dhananjaya de Silva, caught at slip by K.L. Rahul for 21.
India were earlier bowled out after adding just two to their overnight score of 460-9.
Devdutt Padikkal scored 167 while Rahul and Dhruv Jurel hit half-centuries.
INDIA: Shubman Gill (capt.), K.L. Rahul, Yashasvi Jaiswal, Devdutt Padikkal, Rishabh Pant (wkt), Dhruv Jurel, Ravindra Jadeja, Kuldeep Yadav, Manav Suthar, Mohammed Siraj, Prasidh Krishna.
SRI LANKA: Dhananjaya de Silva (capt), Lahiru Udara, Nishan Madushka, Dinesh Chandimal, Kamindu Mendis, Sonal Dinusha, Niroshan Dickwella (wkt), Prabath Jayasuriya, Keshara Nuwantha, Asitha Fernando, Lahiru Kumara.