India, electing to bat on the dry wicket at the Ruhul Amin stadium, were stunned when paceman Mashrafe Mortaza bowled Wasim Jaffer off the first ball of the match.
Captain Rahul Dravid and Dinesh Karthick ensured there were no further setbacks as they hit a century partnership to steer India to 113-1 by lunch on Friday.
Karthick was unbeaten on 54 at the break with the help of eight boundaries.
Dravid was on an unusually aggressive 52, his 47th Test half-century studded with 10 fours.
Jaffer, who was not picked for the preceding one-day series which India won 2-0, shouldered arms to a delivery that swung in sharply and shattered the stumps.
Dravid lifted the pressure with four well-timed boundaries through the covers off Mortaza and Karthick hooked seamer Shahadat Hossain to the square-leg fence.
Mortaza conceded 38 runs in his first spell of five overs as India raced to 67-1 in 11 overs by the first hour.
Runs flowed freely when Bangladesh introduced its two left-arm spinners, Mohammad Rafique and Enamul Haque, into the attack.
Dravid welcomed veteran Rafique by lofting him over the mid-on fielder and later drove him for his 10th boundary.
Earlier, India included five bowlers in a bid to beat the stifling heat and humidity, but sprang a suprise by fielding three seamers in Zaheer Khan, Vikram Rajvir Singh and Rudra Pratap Singh.
Anil Kumble and Test debutant Ramesh Powar formed the spin attack, while Venkatsai Laxman and Yuvraj Singh were the two specialist batsmen to miss out.
Bangladesh left out rookie spinner Mehrab Hossain and fielded two seamers and two spinners.
Brief Scores: India 1st innings: 113 for one wkt at lunch (D. Karthick-Not out 54, R. Dravid-not out 52)