India lost Axar Patel on the last ball of the day. Mehidy Hasan Miraz trapped Axar lbw for 14 runs.
Pujara and Iyer shared a 149-run partnership to reach a respectable total on the opening day.
For Bangladesh, Taijul Islam (3/84) was the most successful bowler. Apart from Taijul, Mehidy Hasan Miraz claimed two wickets and Khaled Ahmed one.
The two-match series forms part of the ICC World Test Championship. India are fourth, having won six of their 12 matches. Bangladesh are in last place with eight defeats from 10 matches. India need to win both matches of the series to stay alive in the race for the World Test Championship final.
Stumps on Day 1⃣ of the first #BANvIND Test!@ShreyasIyer15 remains unbeaten on 8⃣2⃣* as #TeamIndia reach 278/6 a… https://t.co/r83Amoqz3p
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Earlier, Rishabh Pant’s counter-attacking prowess was complemented by Pujara’s obdurance as India recovered to 174 for 4 at tea.
Pant showed the much-needed aggression, hitting six fours and two sixes in his 45-ball, 46-run knock as he along with Pujara (42 not out) added 64 runs after India were reduced to 48 for 3 in the 20th over.
After Pant departed in the post-lunch session, Pujara forged another unfinished 62-run stand off 146 balls with Shreyas Iyer (41 not out) to continue India’s recovery from the early blows.
With the surface more suited to spin, both teams went in with two pacers and three spinners.
Bangladesh vs India: 1st TestStumps, day 1#BCB | #Cricket | #BANvIND https://t.co/rkjcc8C9L3
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The KL Rahul-led India expectedly opted to bat but squandered the opportunity by allowing the Bangladesh bowlers to dominate the proceedings.
Skipper Rahul (22), Shubman Gill (20) and Virat Kohli (1) were the batters to be dismissed. Left-arm spinner Taijul Islam was the standout bowler for Bangladesh as he removed Gill and Kohli.
The aggressive approach that Rahul spoke about ahead of the game was missing in the first session.
Spin was introduced as early as in the sixth over and Rahul greeted his counterpart Shakib Al Hasan with a cut through the point region.
Gill too showed intent with a cut and pull off pacer Ebadot Hossain in the following over as India reached 30 for no loss in seven overs.
However, the boundaries dried up thereafter as Bangladesh bowlers stuck to stump to stump line and stifled the Indians.
Gill perished to a poor shot, an avoidable sweep, while Rahul played away from his body off pacer Khaled Ahmed only to drag it back on to the stumps.
Kohli fell to a beauty from Islam who got one to turn sharply from leg-stump to hit the back leg of the star Indian batter. India went for a review which was unsuccessful.
The top-order batters could have used their feet more against the spinners but preferred to stay back in the crease.
The much-needed attacking approach was displayed once again by Pant who put the pressure back on Islam by smashing him for a couple of fours and a six over wide long-on.
(With PTI inputs)