Anderson then sent Cheteshwar Pujara, whose century helped India post a small first-innings lead, back to the pavilion after rapping him on the back thigh with an inswinger.
Opener Shikhar Dhawan struck three boundaries but never looked comfortable against England's high-calibre seamers and he fell for 17 in Anderson's next over, thick-edging to Ben Stokes at gully after being squared up by a beauty.
Moeen Ali did not have to wait long to get his hands on the ball and he thought he had captured the key wicket of Kohli in his third over when he struck him on the knee roll but umpire Kumar Dharmasena said not out.
England reviewed and looked confident but Kohli was saved by a possible inside edge, although it looked inconclusive.
Earlier, India wrapped up England's second innings for the addition of only 11 runs to leave an absorbing Test balanced on a knife edge.
Broad fell on the first ball of the day, tickling behind off Mohammed Shami who had also taken a wicket with the last ball of the previous day's play.
Curran was run out trying to pinch a second run off a leg bye.
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