India made 436 all out in reply to England's first-innings total of 246, claiming a lead of 190 on day three of the opening Test at Rajiv Gandhi International Stadium on Saturday.
Ravindra Jadeja (87), KL Rahul (86) and Yashasvi Jaiswal (80) scored the bulk of the runs for the hosts.
Part-time spinner Joe Root was the pick of the England bowlers, claiming 4-79.