Put into bat in the Super Eights clash by Bangladesh skipper Najmul Hossain Shanto, the 2007 champions saw five of their top six batsmen reach double-figure scores.
All-rounder Hardik Pandya top-scored with an undefeated 50 off just 27 balls with four boundaries and three sixes.
India had raced to 71-1 in seven overs with skipper Rohit Sharma making a rapid 23 and Virat Kohli hitting his tournament best 37 off 28 balls with one four and three sixes.
The only blip was Suryakumar Yadav, who had hit back-to-back fifties in his last two innings, making just six.
Those runs came off the first of two balls he faced before falling to Tanzim Hasan Shakib who had dismissed Kohli in the same over.
Rishabh Pant cracked 36 off 24 balls with Shivam Dube making 24 with 18 of those runs coming from three sixes.
India beat Afghanistan by 47 runs in their Super Eight opener in Bridgetown while Bangladesh lost to Australia by 28 runs in a rain-hit clash in Antigua.
India have won all four T20 World Cup clashes against their Asian rivals and boast an overall 12-1 head-to-head record.
