After the loss of three wickets in the morning session, West Indies steadied its innings in the second session without conceding any wickets as Powell collected 115 while Chanderpaul added 46.
In the second over after tea, Powell was dismissed on 117 by Bangladesh offspinner Sohag Gazi, who's debut included the wickets of Chris Gayle and Darren Bravo.
But Chanderpaul continued on to his 26th century, reaching 123 not out off 195 balls at stumps. Denesh Ramdin was also unbeaten on 52 off 88 balls.
Gazi's bowling figures stood at 3-97.
Shahadat Hossain, who claimed the wicket of Marlon Samuels (16) in the morning, failed to make any impact in the later sessions.
Gazi removed opener Gayle for 24 and Bravo for 14 to go into lunch on 2-32 from his first 11 test overs after West Indies skipper Darren Sammy won the toss.
Gayle was out when he attempted to send the ball over the long-off fielder, instead providing an easy catch for Mahmudullah.
Bravo was caught by Rubel Hossain at point after he went for a big drive.
Powell's second century in his 12th test came to an end after the ball turned and stayed a bit low to hit the middle stump at 231-4.
Chanderpaul and Ramdin had no trouble playing out the last 28.5 overs, scoring at a run rate of 4.5. Chanderpaul has hit 17 boundaries, and Ramdin five.
Bangladesh has won just three tests from 73 matches since it began playing the long form of the game 12 years ago. Its last test series was nearly 11 months ago when it was comfortably beaten 2-0 at home by Pakistan.