Bangladeshi batsmen Tamim Iqbal and Mushfiqur Rahim put the team in a positive position.
In the first over, Bhuvneshwar Kumar bowled brilliantly and conceded a run and took one wicket -- Soumya Sarkar.
Kedar Jadhav took Tamim's wicket and later sent Mushfiqur back to the pavilion. Ravindra Jadeja took Shakib Al Hasan's wicket bringing India back into the game.
Brief scores: Bangladesh 264/7 in 50 overs (Tamim 70, Mushfiqur 61; Bumrah 2/40)
Arch-rival Pakistan has already booked the berth for itself in the final tie of the tournament after beating England by eight wickets in the first semi-final on Wednesday.
Both India and Bangladesh have lost one match each in the tournament so far -- India lost its match against Sri Lanka, while Bangladesh was beaten by England.
India and Bangladesh have fought some of the most fierce battles in ICC events in the recent past, with India coming victorious on the past two occasions.
First, the 2015 World Cup quarterfinals in Melbourne was a lopsided affair that India won by a mammoth 109 runs. But the second, in the 2016 T20 World Cup, was indeed a close contest, which Bangla Tigers lost to Indians by a single run.