Pace spearhead Jasprit Bumrah took four wickets as India bundled out Bangladesh for 149 to lead by 227 runs on day two of the first Test in Chennai on Friday.
Bangladesh were dismissed in the final session with former skipper Shakib Al Hasan top-scoring on 32 in their reply to India's first-innings total of 376.
The hosts opted not to enforce the follow-on and will bat first in their second innings.
Ravichandran Ashwin had given Bangladesh a challenging first-innings total with his 113 in a marathon 199-run seventh-wicket stand with Ravindra Jadeja.
India's bowlers came out firing and reduced Bangladesh to 40-5 early in the second session after Akash Deep's double strike on successive balls hurt the tourists before lunch.
Bumrah broke through first to send back Shadman Islam bowled for two. Deep then bowled the left-handed Zakir Hasan for three and rattled the stumps of Mominul Haque for a duck.
Mushfiqur Rahim played out the hat-trick ball, but managed just eight runs before he became Bumrah's second wicket of the day.
Shakib and wicketkeeper-batsman Litton Das, who scored 22, put on 51 runs but Jadeja dismissed them both in quick succession with his left-arm spin.
Bumrah kept up the charge with his bouncers and yorkers, and along with Mohammed Siraj helped wipe off the Bangladesh tail with Mehidy Hasan Miraz left unbeaten on 27.
Bangladesh fast bowler Hasan Mahmud finished with figures of 5-83 after rattling the Indian batting on day one, before Ashwin and Jadeja powered a fightback from the hosts.
The pair resumed with India on 339-6 overnight but pace bowler Taskin Ahmed broke the stand early, with Jadeja caught behind without adding to his overnight score of 86.
Deep hit a quickfire 17 with four boundaries before being dismissed by Taskin, who soon got his third with the wicket of hometown hero Ashwin, caught by skipper Najmul Hossain Shanto.
The 38-year-old Ashwin was given a standing ovation after his sixth Test ton, which included 10 fours and two sixes.
Hasan wrapped up the innings with his second five-wicket haul in just his fourth Test.
India are looking to extend their lead at the top of the World Test Championship rankings as they begin a fresh Test season of 10 matches.
Bangladesh have never beaten India in a Test.