Bangladesh captain Shakib al Hasan scored crucial 80 off 85 balls to power his team to score the runs they got after losing wickets at regular intervals.
Though Bangladesh were reduced to 161/6 in 34.1 overs at one point, Towhid Hridoy (54 off 81 balls) and Nasum Ahmed (44 off 45 balls) helped the team to cross the 250-mark.
Shardul Thakur was the best bowler for India as he clinched three three wickets for 65 runs.
India and Sri Lanka have already qualified for the final.