Bangladesh still trail India by 89 runs with four wickets in hand. Taijul Islam (11) was removed off the last ball of the day by Umesh Yadav (2/40).
20 years of Bangladesh cricket: With gritty fans and splendid infrastructure, Tigers still fail to roar
Despite almost 20 years of experience in Tests and having one of the better-looked-after squads, Bangladesh continue to be lambs when they tour overseas
Earlier, the three Indian pacers consistently bowled at 140 kmph, with seam, swing and bounce making life miserable for Bangladeshi batsmen.
India's slip fielding was below-par on the day with Ashwin paying the price for Rahane's twin bloopers in the slip cordon that gave Rahim and Mahmudullah Riyad (10) reprieve.
Senior off-spinner Harbhajan Singh said the onus will be on wicketkeeper Mushfiqur Rahim to lead the side with the bat in the series decider at Nagpur.
Rahim had to endure the heartbreak during Bangladesh's one-run defeat against India in a 2016 World T20 encounter in Bengaluru.
Mushfiqur made 67 while Sabbir added 60 as the duo shared an 111-run partnership for the fifth wicket but Bangladesh stuttered to 223 all out in 41.4 overs replying to Sri Lanka's 314-8.