The 77-run victory for the visitors also ended a 10-match unbeaten run on home soil that began in November 2014.
Put in to bat, India scored an impressive 317 runs for the loss of six wickets. The scoring was led by opening batsman Shikhar Dhawan, who scored 75 and Captain Mahendra Singh Dhoni who hit 69 runs.
The two were ably supported by Ambati Rayudu and Suresh Raina, whose late charge helped India cross the 300 mark.
Raina played his part with the ball too claiming three wickets for 45 runs. India’s leading spinner Ravichandran Ashwin chipped in with two wickets.
Medium pace bowler Dhaval Kulkarni too claimed two wickets while Stuart Binny, Axar Patel and Ambati Rayudu took one wicket each.
Sabbir Rahman was the highest scorer for Bangladesh with 43 with five other batsmen getting out after getting a decent start.
The fall of wickets at regular intervals meant that Bangladesh could reach only 240 runs in 47 overs.
Despite the loss, Bangladesh captain Mashrafe Mortaza was happy with his team’s performance in the series.
"It was the best series of my career. We have achieved more than what we had dreamt of before the series. We had the chance to achieve more, but we could not do so because of some mistakes,” he said after the match.