India fast bowler Akash Deep sent back both Bangladesh's openers inside the first hour of play as the tourists took lunch at 74-2 in the second Test on Friday.
Skipper Najmul Hossain Shanto, on 28, and Mominul Haque, on 17, were batting at the break in Kanpur after putting together 45 runs between them.
Bangladesh openers started cautiously after a wet outfield delayed the match, which could be former skipper Shakib Al Hasan's last outing in the format.
Zakir Hasan stuck around for 24 deliveries before Deep broke through to get the left-hander caught at gully off a diving Yashasvi Jaiswal for a duck.
Deep struck again to trap Shadman Islam lbw for 24 after the umpire denied the call but India reviewed the decision in their favour.
Najmul and fellow left-hander Mominul hung on to the break with a drizzle at the ground bringing out the covers at the stroke of lunch.
The hosts have come in unchanged with three seamers.
Bangladesh ex-captain Shakib, 37, announced his international retirement on Thursday and could be playing his last Test match if he is unable to return home for a slated South Africa series.
Shakib is a former lawmaker for the party of ousted premier Sheikh Hasina and has stayed away from Bangladesh due to the threat of criminal charges levelled against him and dozens of her former allies.
India are highly favoured to sweep the two-match series after winning the opener in Chennai by 280 runs.
Agence France-Presse