Shikhar Dhawan was the best batsman for India scoring 41 off 42 deliveries with three fours and one six.
Bangladesh need to score at a strike rate of 7.45 to win.
Tigers played eight T20Is against India previously but failed to register a single win.
India started well as Rohit Sharma flicked Shafiul Islam for a four off the first delivery of the match. But Bangladesh turned it to their side at the end of the first over when Shafiul trapped Rohit for nine off five balls. Rohit was adjudged lbw after he missed the slower ball seaming in.
India posted 35 in the powerplay losing the wicket of Rohit only. But in the seventh over, Mahmudullah handed over the ball to Aminul Islam Biplob who removed Lokesh Rahul in his first over.
Aminul delivered a slow ball and Lokesh came back before playing a soft shot. Mahmudllah took a regular catch at short cover.
Despite losing two wickets in seven overs, India never looked in trouble because of Shikhar Dhawan. The southpaw was scoring slowly but was a big trouble for the Tigers. However, he fell for 41 during the 15th over in a run-effort by Mahmudullah and Mushfiqur Rahim.
Before Dhawan, Shreyas Iyer scored 22 off 13 balls. His short-term but effective innings was ended by Aminul.
At the end of 15 overs, India were 95 for four. In the last five overs, they amassed 53. Bangladeshi bowlers were most expensive in the last three overs when the conceded 38 runs.
In the seventh-wicket stand, Washington Sundar and Krunal Pandya added 28 runs just in 10 balls.
Eventually, Bangladeshi bowling attack restricted India in 148 for six in 20 overs.
Teenager leg-spinner Aminul was the best bowler of Bangladesh taking two wickets conceding 22 runs in 3 overs. Shafiul also bagged two wickets but he spent 36 runs in four overs. Afif Hossain took one wicket.
Bangladesh (Playing XI): Liton Das, Soumya Sarkar, Mohammad Naim, Mushfiqur Rahim(w), Mahmudullah(c), Afif Hossain, Mosaddek Hossain, Aminul Islam, Shafiul Islam, Mustafizur Rahman, Al-Amin Hossain.
India (Playing XI): Rohit Sharma(c), Shikhar Dhawan, Lokesh Rahul, Shreyas Iyer, Rishabh Pant(w), Krunal Pandya, Shivam Dube, Washington Sundar, Yuzvendra Chahal, Deepak Chahar, K Khaleel Ahmed.