Dravid and Tendulkar were involved in an unbroken stand of 222 runs for the third wicket before the former had to withdraw with injury. Dravid made a solid 111 from 188 deliveries in his 29th ton, inclusive of 11 boundaries.
Tendulkar scored a fluent 143 from 182 deliveries, inclusive of 13 boundaries and a six, before hitting Shakib Al Hasan straight to the midwicket fielder. Murali Vijay eased himself to 30 from 49 deliveries before he hit Shakib straight to the mid-on fielder.
Harbhajan Singh fell off the last delivery of the day as India closed the second day on a comfortable 459 for five in 102.5 overs in their first innings to stretch their lead to 226 runs in reply to Bangladesh's 233.
Indian captain Mahendra Singh Dhoni was batting on 22 at close of play.
Earlier, twin half-centuries by Sehwag and Gambhir gave India to a flying start.
Resuming on his overnight personal score of 41, Sehwag reached his half-century in the third over of the morning with a boundary off Shahadat who, four overs later, had the batsman caught behind. Sehwag needed 61 balls for his quick knock of 56 which he made with the help of seven fours.