Indian spinners never allowed Bangladesh to settle as the Bangladeshis could score just 138/7, which was not enough to challenge India's batting might.
Bangladesh opener Anamul Haque waged a lone battle in the top order by scoring a stroke-filled 44.
Amit Mishra was once again the pick of the Indian bowlers with figures of 3 for 25.
Allrounder Mahmudullah scored 33 not out to take Bangladesh's score past 130.
R Ashwin won the Man-of-the-Match award for his spell of 2 for 15.
Virat Kohli continued his rich form as he top-scored during the run-chase with 57 not out off 50 balls.
Rohit Sharma continued to prove his detractors wrong with a knock of 56.
A collission between Anamul Haque and Sohag Gazi while attempting a catch gave Rohit Sharma a life when he was batting on 36.