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The hosts were chasing 207 to make England bat again, and had raced to 86-0 at lunch but after the break they lost six wickets for 36 runs, BBC reports.
India now hold a lead of 32 runs with one wicket remaining and a day to play.
Ravichandran Ashwin (83) slowed England's progress after Virender Sehwag had made 49, but the tourists will be confident of wrapping up the match on the last day to take a 2-1 lead in the series with one match to play.
Fast bowler Steven Finn, who missed the first two tests with a thigh injury, took the key wickets of Gautam Gambhir and Virat Kohli before trapping Zaheer Khan in front to finish with figures of 3-37.