India were 60 for one at lunch, 223 runs in arrears with Patel on 37 and Cheteshwar Pujara on eight.
Seam bowler Ben Stokes struck in his very first over to get opener Murali Vijay caught behind for 12 as England skipper Alastair Cook juggled with his bowling options.
Patel, who returned to the Indian side after a gap of eight years, batted with purpose while opening the innings in place of the injured Lokesh Rahul.
The left-handed batsman also got a caught behind decision reversed in his favour after replays showed that Chris Woakes' delivery had grazed his shirt and not his bat when he was on 12.
Patel tackled the England bowlers with the right balance of caution and aggression as he hit six boundaries in facing 73 balls.
The visitors, who resumed the day on 268 for 8, were bowled out inside four overs with India's Mohammed Shami claiming three wickets in the innings.
Overnight batsmen Adil Rashid (4) and Gareth Batty (1) did not last long but number 11 James Anderson managed an unbeaten 13.
On Saturday, Jonny Bairstow's gritty 89 gave England's total some respectability after they elected to bat first on a pitch that is expected to turn as the match progresses.
After being reduced to 87 for 4 before lunch and then 144-5, the lower-order rallied around Bairstow who formed crucial partnerships with Ben Stokes (29) and Jos Buttler (43).
India's Umesh Yadav, Ravindra Jadeja and Jayant Yadav took two wickets each.
India lead the five-match series 1-0.