Opener Jack Crawley top-scored with 60, but the rest of England's batting faltered against India's spin, with Ashwin taking 5-51 and Kuldeep Yadav taking 4-22.
England lost regular wickets to end their innings in the final session, leaving the onus on the bowlers to level the series and send it to the decider of the fifth Test in Dharamsala.
India's bowlers did the job after wicketkeeper Dhruv Jurel's 90-run knock in the morning session to reduce the hosts' deficit after starting the day at 219-7.
Ashwin took the new ball on a pitch with cracks and variable bounce and hit successive deliveries to dismiss Ben Duckett, caught at short leg for 15, and Ollie Pope LBW without scoring, leaving England 19–2. Lag behind.