Mayank Agarwal reached the three-digit mark with the help of 15 boundaries.
Earlier, India wrapped up the visitors at 150 in their first innings. Bangladesh won the toss and chose to bat first. Mushfiqur Rahim was the top scorer with 43 and Mominul Haque contributed 37.
For India, Mohammed Shami took three wickets and Ishant Sharma, Ravichandran Ashwin and Umesh Yadav claimed two each.