India lost three wickets after the lunch break and were 256 for six at tea on the first day of the first test in Chennai on Thursday.
Yashasvi Jaiswal added 62 runs with Rishabh Pant and 48 with KL Rahul to prop up the hosts, who had slumped to 34-3 inside the opening hour on a lively track at the M.A.Chidambaram Stadium.
Ravichandran Ashwin (21) and Ravindra Jadeja (seven) were leading India's push for a 200-plus total with their unbroken stand of 32.
Bangladesh are on a high after their 2-0 series sweep in Pakistan earlier this month and looked in charge after seamer Hasan Mahmud's (4-35) three-wicket burst in the morning session.
Touring captain Najmul Hossain Shanto elected to field, hoping his seamers would milk the early morning conditions and his new ball pair of Hasan and Taskin Ahmed did not let him down.
India captain Rohit Sharma (six) needed 11 balls to get off the mark and survived a vociferous lbw appeal before edging Hasan to Shanto at second slip.
In his next over, Hasan had Shubman Gill caught behind for a duck tickling the ball down the leg side.
Virat Kohli also fell to a soft dismissal, driving away from his body to be caught behind for six.
Challenging conditions and departing partners could not bog down Jaiswal though, and the opener played gorgeous drives and exquisite flicks.
Pant, playing his first test since a horrific car crash in December 2022, cut and pulled fearlessly and scored briskly to turn the heat back on the bowlers.
Hasan broke the 62-run stand soon after the lunch break when Pant's (39) lazy waft to a delivery wide outside the off-stump led to another soft dismissal.
Nahid Rana ended Jaiswal's fluent knock of 56 with a peach of a delivery which the batter could only guide to first slip.
Spinner Mehidy Hasan Miraz removed Rahul for 16 before Ashwin counterattacked.
