Dimuth Karunaratne was batting on 55 and Kusal Mendis on 61 at the break with Sri Lanka, still 321 runs behind, facing an uphill task to save the match on a fast-crumbling track.
Upul Tharanga, who made a duck in the first innings, managed two in the second before falling to Umesh Yadav.
Earlier, Ravichandran Ashwin (5-69) claimed his 26th five-wicket haul as he and spin partner Ravindra Jadeja (2-84) helped rout Sri Lanka for 183 on a day three pitch that allowed for prodigious spin, with the ball often kicking up puffs of dust.
Niroshan Dickwella topscored with a desperate 51 as Sri Lanka lost their remaining eight wickets in an extended morning session to find themselves staring at a 439-run first-innings deficit and series loss with a match to spare.
India captain Virat Kohli, who led his team to a crushing 304-run win in the first of the three tests, was rewarded for his superb field placement when avid sweeper Dinesh Chandimal sent a Raviindra Jadeja delivery straight to Hardik Pandya at square leg. Chandimal made 10.
Jadeja was denied a second success in that over when Kohli dropped Angelo Mathews with the former Sri Lanka skipper having yet to score.
Kohli soon made amends, running backwards to take a brilliant catch to send back Kusal Mendis, who had made 24 before Yadav induced the leading edge.
Mathews decided to hit his way out of the trouble and clobbered a couple of sixes off Jadeja but the ploy did not work for long.
With a breezy 26 on the board, he flicked at an Ashwin delivery and Pujara took a spectacular left-handed catch at leg gully.
Jadeja dismissed Dhananjaya de Silva for a golden duck and Mohammed Shami came up with a two-wicket over to leave the Sri Lankan innings in tatters.
Realising the futility of trying to hang around, Dickwella threw his bat at everything, hitting seven boundaries and a six before attempting an ugly scoop against Shami that deflected the ball onto his stumps.
Nuwan Pradeep came out to bat despite a hamstring injury which will rule him out of the remainder of the series and he faced six balls before falling for a duck to end the innings.
(Reporting by Amlan Chakraborty in New Delhi; editing by Nick Mulvenney)
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