Mishra, who took just one wicket and looked unimpressive in the England first innings, took wickets in his first two overs to remove debutant opener Haseeb Hameed (82) and then pack off top batsman Joe Root (4) cheaply to bring some interest into the match.
England captain Alastair Cook was, however, holding fort at one end after compiling his 30th century of his 136-Test-old career which was also his sixth against India and fifth in this country to show his liking of Indian conditions.
The not out batsman at the other end was Ben Stokes on 6, even as Test looked headed for a draw. The tourists added 97 runs in 29 overs during the first session.
The visitors, appearing to play for a draw on the last morning of the game, all of a sudden changed their approach and started to go after the Indian bowling, losing two wickets too in the process.
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Replays were called for as Mishra was thought to have over-stepped but he had landed his front foot inside the crease by the barest margin and Hameed, who played spin and pace with equal felicity, departed after having added 180 runs with his captain for the first wicket.
In the first hour of play, England showed little intent on getting quick runs. With the wicket playing easy, Cook and Hameed had no trouble in facing the pace-cum-spin attack employed by the hosts.
India, too, employed a semi defensive field and kept Ravichandran Ashwin operating from one end for the first hour and he kept things in check although hardly causing any discomfort to the two batsmen.
India alternated between Mohammed Shami and Umesh Yadav at the other end and the first hour's play saw Cook reach 50 in 122 balls. It contained just three hits to the fence.
Ashwin was replaced after an economical 9-over spell for 17 runs by Ravindra Jadeja while Mishra replaced Yadav after the pacer had conceded 23 runs in six overs.
The move paid off immediately as Mishra caught and bowled Hameed. Root followed Hameed into the pavilion before England adjourned for lunch without losing another wicket.