Bangladesh was put into bat and posted 120-5 in a rain-hit game that was reduced from 20 to 15 overs after a two-hour delay.
India won with seven balls to spare, reaching 122-2 as skipper Mahendra Singh Dhoni smashed a towering mid-wicket six to finish the game.
Dhawan and Virat Kohli combined for a 94-run partnership for the second wicket after India was reduced to 5-1.
Kohli was unbeaten on 41, while Dhoni was on 20. Mahmudullah smashed an unbeaten 33 for Bangladesh. (Courtesy AP)