Chasing 223 runs, India got off to a good start and at the end of 50 overs, managed to reach their target having lost seven wickets.
The highest scorer for India was Captain Rohit Sharma who scored 48 runs in 55 balls with three sixes and three boundaries.
However, after Sharma’s dismissal, Mahendra Sing Dhoni and Dinesh Karthik together scored 54 runs paving the way for India to reach their victory target.
Although Bangladesh managed to send the first five Indian batsman to the pavilion within 167 runs Ravindra Jadeja (23) and Bhuvenshwar Kumar (21) brought the target within India's reach through a 45-run stand for the sixth wicket but Bangladesh removed them both with eight runs still needed.
India then required six off the last over and one off the final delivery which came as a leg-bye. Kedar Jadhav finished with 23 not out.
The wickets were divided two each between Mustafizur Rahman and Rubel Hossain.
India won the toss and invited Bangladesh to bat first and Bangladesh scored 222 runs in 48.3 overs having lost all their wickets.
Liton Das who played an excellent game and held the innings together during his 117-ball 121 which featured a dozen boundaries and two sixes but Bangladesh, who were put into bat, were all out in 48.3 overs despite a solid opening stand of 120 with Mehidy Hasan.
Only Liton Das Mehedi Hasan and Soumya Sarkar managed to score while the rest could not get past the 10 runs mark.
Kuldeep Yadav bowled excellently and clinched three wickets for 45 while Kedar Jadhav got two wickets for 41.
Liton was adjudged the man of the match in the final game while Shikhar Dhawan was adjudged the man of the series.