The tourists, who trail 2-1 in the four-match series, began their second innings 160 runs behind India and were promptly reduced to 65 for six, with Joe Root the only one of the top five to pass five.
Earlier, India, resuming on 294 for seven overnight, had pressed home their advantage thanks in large part to an eighth-wicket century stand between Axar Patel and Washington Sundar.
The latter looked on course for a maiden Test century, but when Patel was run out for 43, both Ishant Sharma and Mohammed Siraj fell quickly to Ben Stokes for nought, leaving Washington stranded on 96 not out as the home side were bowled out for 360.
Neither England opener had made it into double figures in the first innings and neither ever looked likely to here, either, Zak Crawley edging Ravi Ashwin to Ajinkya Rahane at slip, while Dom Sibley saw a powerful sweep ricochet off short-leg and into the gloves of wicketkeeper Rishabh Pant.
In between, Jonny Bairstow’s disastrous series continued as he was dismissed first ball for a third duck in four innings and Ben Stokes, who had showed signs of a return to form with a first innings half-century, soon followed, miscuing to leg slip for two.
At that point, England were 30 for four, before a partnership between Ollie Pope and Root offered brief resistance.
The former hit Ashwin over long-on for one glorious six, but the Surrey man was soon on his way thanks to some superb glove work from Pant, stumped off Patel for 15.
Root was trapped lbw by Ashwin two balls later, leaving Dan Lawrence and Ben Foakes to shepherd England to tea 91 for six, still 69 runs adrift.