Washington Sundar struck once in each of his first three overs to leave Bangladesh in trouble as the Tigers chase 177 in their Nidahas Trophy game on Wednesday.
Bangladesh are now on 57 for 3 after 8 overs, with Mushfiqur Rahim on 11 and skipper Mahmudullah on 10.
Opener Liton Das and Soumya Sarkar fell cheaply, but Tamim Iqbal did make a promising start. However, he misjudged a Sundar delivery to depart on 27, made in 19 balls with four fours and a six.
Put into bat first, opener Rohit Sharma hit 89 off 61 balls to lead India to 176 for 3.
The Indian skipper slammed five fours and five sixes in his innings, but he might have felt dejected as the overs ran out, depriving him of a chance to hit his third T20 international ton.
Openers Rohit and Shikhar Dhawan made 70 in the first wicket to give the Indians an ideal start.
Paceman Rubel Hossain bowled the latter to break the stand, but Rohit then added another 102 in the third-wicket partnership with Suresh Raina.
The impressive Rubel removed Raina in the first ball of the innings' last over, which saw only four runs
Raina hit 47 off 30 balls, with five fours and two sixes.