Tamim Iqbal scored 70 runs and Nasir Hossain 54 while Praveen Kumar took three wickets as Bangladesh overhauled the victory target in 49.2 overs for the loss of 5 wickets.
Earlier India set Bangladesh a target of 290 to clinch their one day international (ODI) cricket match of Asia Cup.
Sachin Tendulkar top-scored for India with 114 as the India made 289-5 after losing the toss. Mashrafe Mortaza with 2-44 was Bangladesh's most impressive bowler.