Pacer Akash Deep and Ravichandran Ashwin dismissed Bangladesh captain Najmul Hossain Shanto before rain interrupted the match on the opening day of the second Test in Kanpur on Friday.
The weather forecast suggested that rain would be a factor from the start.
Only 35 overs were bowled after Rohit Sharma chose to bowl first in cloudy conditions.
Bangladesh struggled to reach 107 for three, with Shanto scoring 31.
Mominul Haque was at 40 not out, while veteran Mushfiqur Rahim had just 6 runs when the rain started.
The match had a delayed start due to overnight rain.
The heavy cloud cover pushed India’s team selection, leading to the decision to include all three pace bowlers from the previous Test, which meant that local favourite Kuldeep Yadav was left out again.
Akash Deep, who took 2 wickets for 14 runs in 10 overs, bowled effectively, consistently hitting good lengths and making the ball move. Shanto, batting positively, tried to ensure Bangladesh didn't fall behind early on.
The Indian bowlers, especially Jasprit Bumrah and Mohammed Siraj, kept the Bangladesh openers cautious.
Shadman Islam managed to score 24 runs but Zakir Hasan struggled and was dismissed for a duck. Akash ended Hasan's struggle by getting an edge that was caught by Yashasvi Jaiswal.
Akash also sent Shadman back leg before wicket, although Shadman reviewed the decision without success.
Shanto started strong, hitting a couple of boundaries, but fell to Ashwin, who trapped him in the third over of the second session after Shanto was deceived by the turn.
Mominul gained confidence, hitting two boundaries in one over from Akash and helping Bangladesh cross the hundred mark.
However, just nine overs into the second session, bad light halted play, and a light drizzle quickly turned into heavy rain, forcing the players off the field.