New Delhi: Ravind Jadeja picked up two wickets in last over to leave the tourists reeling at 31 for 3 at Feroz Shah Kotla Ground, Delhi on Tuesday.
Dhananjaya de Silva was unbeaten on 13 with Angelo Mathews not out on Zero.
India have been relentless in their attack, brought about by the luxury of defending 400 plus.
Shami was fast and hostile, Ishant was steady and Jadeja was robotic in what he does.
There are enough signs of variable bounce on this surface and batting will only get difficult tomorrow.
Mohammed Shami and Ravindra Jadeja ripped through Sri Lanka's top order after India set them 410 to win the Delhi Test or survive the best part of four sessions to save it.
Bad light brought the fourth day to an end with a theoretical 13 overs remaining, with Sri Lanka struggling at 31 for 3.
Earlier, Rohit Sharma completed his half-century as India set Sri Lanka a daunting 410 to win the pollution-tainted third Test in New Delhi that saw paceman Suranga Lakmal vomit twice on the ground Tuesday.
The highest successful run chase in the fourth innings of a Test was by the West Indies who defeated Australia after making 418 in 2003.
Skipper Virat Kohli (50) declared India's second innings on 246-5 after Sharma reached his half-century in the final session on day four at the smog-shrouded Feroz Shah Kotla ground.
Sri Lankan fast bowler Lakmal, who was forced to return briefly to the dressing room after vomiting twice while fielding, bowled 14 overs and claimed a wicket.
Groundsmen rushed in to cover the spot with sand and sawdust as air pollution in the Indian capital took centre stage for the fourth day in a row.
A doctor at the stadium examined three Sri Lankan players and said their vitals were normal.
For India, opener Shikhar Dhawan top-scored with 67 on a run-filled wicket. Lahiru Gamage, Dilruwan Perera, Lakshan Sandakan and Dhananjaya de Silva took a wicket each.
Earlier, Sri Lanka were dismissed for 373, conceding a 163-run lead to India, who had declared at 536 for seven.
But it was the hazardous smog in one of the world's most polluted cities that again dominated proceedings.