But the hosts also suffered a blow, with Chris Woakes in danger of missing the rest of the match after damaging his shoulder in a fall while fielding on the boundary edge late in the day.
He was led back to the dressing room in a makeshift sling amid fears of a dislocation. A scan was being arranged to determine the extent of the damage with further updates expected on Friday morning.
It came after England had worked hard for their breakthroughs and they will be delighted to have got rid of KL Rahul, Ravindra Jadeja and Shubman Gill, the men who have tormented them throughout the summer, though captain Gill gifted his wicket with a suicidal run-out.
Even though there are four days remaining, India's chances of fighting their way into a position where they could force a victory already look extremely slim.
The overcast morning conditions on Thursday had looked ideal for England's all-seam attack, even without injured captain Ben Stokes, but they lacked a cutting edge.
Recalled Gus Atkinson trapped Yashasvi Jaiswal lbw for two as stand-in captain Ollie Pope finally got on the right side of a DRS review after 14 unsuccessful appeals last year.
Rahul, with over 500 runs to his name from the first four matches, looked relatively untroubled before playing-on to Chris Woakes for 14 as India reached lunch on 2-72.
Gill, averaging over 90 and with four centuries to his name in the series, then inexplicably set off for a non-existent single and was run out by four yards as bowler Atkinson had time to transfer the ball to his right hand before throwing down the stumps.
Gill had started the day with all sorts of records in his sights but, by adding only 21, he achieved only a couple as his tally of 743 took him beyond West Indies' Garfield Sobers (722 in 1966) as the highest-scoring visiting captain.
It also moved him into the top nine for the most runs scored in a series in England - either for or against the hosts.
After a rain-delayed restart, a wayward Josh Tongue, whose first over lasted nine balls and went for 12 runs, finally found his line to nip the edge of Sai Sudharsan's bat to dismiss him for 38.
Tongue repeated the feat soon afterwards to remove Jadeja for nine and India were reeling on 5-123 with their big-hitters all gone, or in the case of Rishabh Pant, absent through injury.
Dhruv Jurel, a ball after overturning an lbw decision against him, then got tucked up by Atkinson and was caught neatly at second slip by Harry Brook for 19.
Karun Nair batted calmly to finish on 52 not out and Washington Sundar was on 19 at the close as the impressive Atkinson finished the day with figures of 2-31 off 19 overs.
