India lost the wicket of captain Virat Kohli late in the day after he had put on 64 runs for the third wicket with Rohit Sharma, who was batting on 57 (off 82 balls) at stumps.
India had earlier lost Shubman Gill and Cheteshwar Pujara early, both falling within six balls.
Gill and Sharma had survived the new ball in twilight period.
India, who had gone into the dinner break at five runs for no loss in five overs, had added 94 in the last session, losing all three wickets that fell on the opening day.
Earlier, Patel took six wickets and off-spinner Ravichandran Ashwin bagged three to hasten the end of England's first innings.
Opener Zak Crawley was the top-scorer for England with 53 -- the solitary half-century of the innings. The next highest score was captain Joe Root's 17.
Brief scores: England: 112 all out in 48.4 overs (Zak Crawley 53, Joe Root 17; Axar Patel 6/38, R Ashwin 3/6) India 99/3 (R Sharma 57 batting, J Leach 2/27)