Another pacer, Jaydev Unadkat, took the other two wickets in his first test in 12 years.
Bangladesh was dismissed for 227 in its first innings and India reached 19 for no loss before bad light brought a premature end to the day with six overs remaining.
Shubman Gill was batting on 14 with captain KL Rahul on 3 after surviving a leg-before decision.
Mominul Haque, one of two changes by Bangladesh after heavy defeat in the first test last weekend, made a team-high 84 and was the ninth batter out. The home side lost its last five wickets for just 14 runs.
Most of the Bangladeshis made starts but failed to carry on on an otherwise good batting track. Mushfiqur Rahim made 26 and Liton Das added 25.
“It is very frustrating,” Bangladesh batting coach Jamie Siddons said. “We work hard. We talk about when you’re in, you need to stay in. You have to make sure of a big score when you get a start.
“People made mental errors again when they were set. The ball was spinning but the pace bowlers weren’t getting off a great deal. To let Umesh get five wickets (four wickets) was very disappointing.”
Mominul, who replaced Yasir Ali, was dropped on 11 by wicketkeeper Rishabh Pant off Ashwin (4-72).
However, Ashwin had Mominul caught by Pant when the batter’s glove was nicked trying to leave a turning delivery. He hit 12 fours and one six in his knock, playing 157 balls.
“Mominul had a more positive approach rather than thinking he was going to get bad balls,” Siddons said. “He was thinking I am going to score today. You have a better chance of having success when you do that.”
Mominul played a disciplined India bowling attack with utmost confidence to keep the scoreboard ticking amid wickets tumbling around him.
After opting to bat first, Bangladesh openers Najmul Hossain and Zakir Hasan combined for 39 but both of them were dismissed in the space of three balls.
Unadkat made the breakthrough when he dismissed Zakir for 15 with a delivery that carried extra bounce.
Zakir, who made a century on debut in the first test, could have gone for a duck had Mohammed Siraj not dropped him at backward square leg off Yadav in the second over of the day.
Najmul went on 24 after offering no shot against Ashwin.
Captain Shakib Al Hasan joined Mominul and played some aggressive shots. But he went for one shot too many as he lobbed one straight to Cheteshwar Pujara at mid off and gave Yadav (4-25) his first wicket.
“The Bangladesh batters got starts but you have to be patient on this kind of a wicket. I think they played too many shots,” Yadav said.
“They are trying to play positive cricket because that is their style. We just bowled in the right areas.”
Mushfiqur and Liton started well but were out while set in the crease.
Mushfiqur was caught behind to an Unadkat length delivery that moved slightly. Liton played some beautiful shots around the wicket then chipped it straight to Rahul at midwicket off Ashwin.
In between, Mominul raised his 16th test fifty off 78 balls with a fierce cut towards backward point for four against Unadkat.
Yadav found reverse swing in the final session and accounted for Mehidy Hasan Miraz (16) and Nurul Hasan Sohan (6).
Ashwin cleaned up the tail, spinning the balls viciously.
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