This is also Bangladesh's highest score against India in ODIs, surpassing the previous best of 296 for six at the same venue in 2010.
Openers Soumya Sarkar (54 off 40 balls) and Tamim Iqbal (60 off 62 balls) added 102 runs for the opening stand in only 13.4 overs to lay a solid foundation.
Shakib al Hasan (52 off 68 balls), Sabbir Rahaman (41 off 44 balls) and Nasir Hossain (34) batted well in the middle-order to take Bangladesh to a substantial total.
Ravindra Jadeja (1/48) was good in patches and Bhuvneshwar Kumar (2/37 in 7 overs) ended with a decent outing.
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The Indian bowlers somewhat redeemed themselves in the final 10 overs in which Bangladesh scored only 57 runs and lost the last five wickets for only 40 runs.
Bangladesh openers Sarkar and Tamim started in a whirlwind fashion after their skipper Mashrafe Mortaza opted to bat on a good surface.
When Ashwin was initially brought into the attack, Sarkar lofted him over deep midwicket for a huge six. The coveted half-century came off 38 balls when he just guided a delivery from Mohit over keeper's head for a one bounce four.
To be fair to Tamim, once he got a couple of boundaries, he also matched his junior colleague stroke for stroke even though Sarkar's batting was more pleasing to the eye.