India lost the wicket of opener Mayank Agarwal to the bowling of Al-Amin Hossain but then Rohit Sharma and Cheteshwar Pujara held on to their wickets.
India scored 35-1 in their 12 overs and they trail Bangladesh by 71 runs.
Bangaldesh's opening bowlers Al-Amin and Abu Jayed Rahi bowled with good control, and Rahi threatened to take the wicket of Rohit, who looked restless against the swing of the pink ball.
Rohit should have be dismissed for 12 runs in the last over before tea as Rahi forced him to play a pull shot and the ball went to the deep square leg fielder, Al-Amin, who dropped a sitter.
Bangladesh 1st Innings
Bangladesh lost all their wickets for just 106 runs after lasting only 30.3 overs in the first innings as Indian bowlers dominated.
Ishant Sharma was the pick of the bowlers as he took 5-22 from his 12 overs while Mohammad Shami was excellent as usual, taking 2-36 off his 10.3 overs.
Umesh Yadav bowled seven overs and took three wickets for 29 runs to ensure all the wickets were taken by pacers and Bangladesh never managed to pose a threat with the bat.
Earler in the second session, Liton Das who scored 24 runs had retired hurt after being hit on the helmet by a Shami bouncer and Mehidy Hasan Miraz replaced him as the concussion substitute.
Miraz scored eight runs while the main resistance from the lower order came from Nayeem Hasan, who scored 19 runs before being dismissed by Ishant.
Bangladesh lose six top order batsmen and are struggling at 73-6 against India in the first day of the second Test at Kolkata.
Indian pacers once again wrecked havoc and used the extra swing of the pink ball to good effect.
Imrul Kayes (4), Mohammad Mithun (0), Mominul Haque (0) and Mushfiqur Rahim (0) all departed cheaply.
Shadman Islam got a start, playing some good shots, but soon departed after fishing at a good-length ball to be out for 29.
Mahmudullah was the next batsman to depart as he too planted his bat at a rising length ball he could have left, and Wriddhiman Saha took a brilliant catch to dismiss him for six runs.
Liton Das was struck on the helmet a by a well directed, Mohammad Shami bouncer and after a few overs, he retired hurt as the supper break was taken.
It remains to be seen if Liton will be able to bat again or else Bangladesh are effectively 73-7.
Bangladesh have won the toss at the Eden Gardens and elected to bat first.
Bangladesh have two changes as Al-Amin Hossain and Nayeem Hasan comes in for Mehidy Hasan and Taijul Islam.
India have no changes to their team.
After the toss, two sides were ceremonially introduced to Bangladesh Prime Minister Sheikh Hasina. The Premier is at the Eden Gardens to witness the historic Test match.
Bangladesh PM also started the proceedings by ringing the bell at the Eden Gardens before the match.
Both India and Bangladesh are playing their first-ever Test match under the lights and with the Pink ball.
Bangladesh: Imrul Kayes, Shadman Islam, Mominul Haque(c), Mushfiqur Rahim, Mohammad Mithun, Liton Das (wk), Mahmudullah Riyad, Nayeem Hasan, Abu Jayed Rahi, Ebadat Hossain, Al-Amin Hossain
India: Rohit Sharma, Mayank Agarwal, Cheteshwar Pujara, Virat Kohli (c), Ajinkya Rahane, Ravindra Jadeja, Wriddhiman Saha (wk), Ravichandran Ashwin, Umesh Yadav, Mohammad Shami, Ishant Sharma