The match was cut into a 15-over affair after rain coupled with gusty winds delayed the start for two hours. Rain hit the stadium around 6:15pm (12:15GMT), about 1:15 hours before the scheduled beginning of the match.
Thousands of fans who spent hours in the queues to collect tickets for the match were drenched or forced to take shelter under the galleries due to the unexpected downpour. A 20-minute power failure, which followed the rain, only made the matter worse.
Earlier, India won the toss and elected to field first.
Both Mahmudullah and Sabbir Rehman remain unbeaten on 33 and 32 runs. Pick of the bowlers was Ravichandran Ashwin who took one wicket and gave 14 runs in three overs,
Batting first, the start was not ideal for Bangladesh. They were 30 for the lost of two wickets and 68 for three after 10 overs. They made 48 runs in last five overs.
India need 121 runs in 90 balls to win the Asia Cup T20 for the sixth time and it would be the first time that Bangladesh will become an Asian champion if they successfully restrict India under 121.