An hour's play was lost in the session following light rain during the lunch break, forcing the umpires to call tea 30 minutes late in a bid to make up for lost time.
Opener Dinesh Karthick and captain Rahul Dravid, who hit half-centuries before lunch after the first-ball dismissal of Wasim Jaffer, departed in the space of 12 balls when play resumed.
The duo, which put on 113 for the second wicket by lunch, took the total to 124 when Karthick (56) played a rash drive off Mashrafe Mortaza and holed out to Mohammad Ashraful at mid-off.
Karthick's third Test 50 contained nine boundaries.
Dravid made 61 when he top-edged a cut off seamer Shahadat Hossain and was caught behind by wicket-keeper Khaled Mashud as India went from 124-1 to 132-3.
Sachin Tendulkar (35 not out) and Sourav Ganguly (16 not out) were together at tea, having put on 49 runs for the fourth wicket.
India, electing to bat on the barren wicket at the Ruhul Amin stadium, were stunned when Mortaza bowled Jaffer off the first ball of the match.
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 Shahadat to the square-leg fence.
The scoring rate slowed down after lunch following the dismissals of Dravid and Karthick as Tendulkar and Ganguly took time to settle down on a wicket that offered little assistance to the bowlers.
India included five bowlers to beat the stifling heat and humidity, but sprang a surprise 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: Total 181 for 3 at tea ( Karthick 56, Dravid 61, Tendulkar 35 (batting), Ganguly 16 (batting)
Fall of wkts: 1-0, 2-124, 3-132