A counter-attacking century from Ravichandran Ashwin pulled India to 339-6 on day one of the first test after Bangladesh fast bowler Hasan Mahmud rattled the hosts with four wickets on Thursday.
India slipped to 34-3 inside the first hour of play in Chennai then 144-6 in the second session before Ashwin, on 102, and Ravindra Jadeja, on 86, put on an unbeaten stand of 195 runs.
Hasan had vindicated skipper Najmul Hossain Shanto's decision to field first in overcast conditions, striking early with three wickets and took one more after lunch.
The tourists, fresh from their 2-0 sweep in Pakistan, are looking for their first-ever test win against India.
Chennai-born Ashwin and the left-handed Jadeja – India's go-to spinners – blunted the Bangladesh bowling, to the delight of the home fans.
Ashwin, 38, reached his sixth test ton in 108 balls with 12 boundaries, removing his helmet and raising his hands to soak in the crowd's cheers.
Hasan ripped through the Indian top-order including skipper Rohit Sharma and Virat Kohli – both scoring just six runs – to leave the hosts at 34-3 inside the first hour of play.
Opener Yashasvi Jaiswal, who made 56, put on a 62-run partnership with fellow left-hander Rishabh Pant to get some momentum into the Indian innings.
Hasan broke the stand in the third over after lunch when wicketkeeper-batsman Pant, who is playing his first test after a serious 2022 car crash, was caught behind off a loose shot. He made 39 with six boundaries.
Jaiswal fell to Bangladesh's new pace sensation Nahid Rana. Spinner Mehidy Hasan Miraz then took down KL Rahul for 16.
Hasan's opening spell of 3-14 put the hosts immediately on the back foot, starting with Rohit caught at second slip.
Shubman Gill survived just eight deliveries before being caught behind for a duck when he attempted a flick down the leg side.
Kohli walked in to loud cheers but the noise soon stopped when the former captain edged a length delivery outside the off-stump from Hasan to wicketkeeper Litton Das.
It was a disappointing outing for Kohli after missing his team's 4-1 home win over England in March due to the birth of his second child.
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.
The second and final test starts on September 27 at Kanpur.
BANGLADESH: Shadman Islam, Zakir Hasan, Najmul Hossain Shanto (captain), Mominul Haque, Mushfiqur Rahim, 6 Shakib Al Hasan, Litton Das (wicketkeeper), Mehidy Hasan Miraz, Hasan Mahmud, Nahid Rana, Taskin Ahmed
INDIA: Rohit Sharma (captain), Yashasvi Jaiswal, Shubman Gill, Virat Kohli, KL Rahul, Rishabh Pant (wicketkeeper), Ravindra Jadeja, Ravichandran Ashwin, Jasprit Bumrah, Akash Deep, Mohammed Siraj