India set Bangladesh a target of 415 runs to win the first cricket Test in Chittagong on Wednesday.
India declared their second innings at 413 for eight shortly after tea on the fourth day.
VVS Laxman remained unbeaten on 69 off 89 balls while Gautam Gambhir (116) scored his ninth Test century in the morning session.
After lunch, India lost the wickets of Sachin Tendulkar (16), Yuvraj Singh (25) and Dinesh Karthik (27). Laxman stayed solid at the other end taking 72 balls for his 50.
India led by 385 runs at tea and added another 30 before calling off the innings.
Earlier, Gambhir scored his fifth Test century in a row. His 129-ball 116 had 10 fours and a six.
Resuming at 122/1, India scored 137 runs in the morning session from 31.4 overs.
Gambhir got good support from night watchman Amit Mishra, who scored his maiden Test half-century. Gambhir and Mishra added 98 runs for the second wicket.
Mishra was the first to be dismissed in the morning when he charged down the track, trying to clear mid-off, but was caught by Tamim Iqbal. His 70-ball 50 was studded with six fours.
Gambhir got a life when he was dropped on 55. He was finally dismissed holing out in the deep to Shariar Nafees off debutant pacer Shafiul Islam.
Dravid made a 50-ball 24 before he was run out just before lunch.