Umesh Yadav (3-49) dismissed England's in-form captain Joe Root late on Thursday to help India claw their way back into the contest after the tourists folded for 191 in the first innings.
The seamer, playing his first match of the series, struck twice after England resumed the second day on 53-3.
Nightwatchman Craig Overton was the first to go, snared at first slip by India captain Virat Kohli.
Dawid Malan, who made 31, followed suit after Rohit Sharma at second slip dived to his right to take a sharp catch.
The Indian seamers, who had been bowling with lot of discipline, suddenly took their foot off the pedal and boundaries started flowing.
Pope looked in particularly good shape and hit Shardul Thakur for three boundaries in the same over.
His aggression appeared to rub off on Bairstow who meted out similar treatment to Mohammed Siraj in the next over.
The five-test series is level at 1-1.