India lost Rohit Sharma in their chase for 420 after Ravichandran Ashwin took six wickets to dismiss England for 178 on day four of the opening Test on Monday (8).
The hosts reached 39 for one at stumps after spinner Jack Leach bowled Sharma for 12 on a deteriorating Chennai pitch.
Shubman Gill, on 15, and Cheteshwar Pujara, on 12, were batting at the close with India needing another 381 runs to win the first of the four Tests.
On a dominant day for spinners, Ashwin claimed his 28th five-wicket haul in England's second innings.
The off-spinner sent back Rory Burns with the first ball of the innings and struck crucial blows, including taking Ben Stokes for seven.
Skipper Joe Root top-scored with 40 off 32 deliveries. He hit 218 in the first innings of his 100th Test.
Root hit seven boundaries before being trapped lbw by paceman Jasprit Bumrah. Ollie Pope (28) and Dom Bess (25) also helped England build a big lead.
Left-arm spinner Shahbaz Nadeem took two wickets and got wicketkeeper-batsman Jos Buttler stumped for 24. Dan Lawrence (18) was Ishant Sharma's 300th Test wicket.
India were bowled out for 337 in their first innings in the morning session, 42 runs short of avoiding the follow on despite Washington Sundar's unbeaten 85.
England, who scored 578 in their first innings, decided against making the home side bat again.
Leach and paceman James Anderson took two wickets each in the morning session to pack off India after the hosts started the day 257-6.
Sundar, who made his debut in the fourth Test of India's historic win in Australia last month, put on 80 runs with overnight partner Ashwin, who made 31.
Norris capitalised on the incident to take the lead and hold on for victory. Getty Images 
