A brief 35-run partnership between Chris Woakes and Joe Root kept England alive before Shardul Thakur had the England captain playing on to the stumps. Chris Woakes was dismissed at the stroke of tea by Umesh Yadav.
Victory will take India 2-1 up in the series with one Test to go.
Brief scores (Tea, Day 5)
India 191 and 466 vs England 290 and 193/8 in 84.1 overs (R Burns 50, H Hameed 63, J Root 36, J Bumrah 2/24, R Jadeja 2/50, S Thakur 2/22)