Opener Powell batted until just after tea for 117, his second Test ton, with Chanderpaul unbeaten on 123 as the Windies recovered well from losing three wickets in the morning session to close on 361 for four.
Debutant spinner Sohag Gazi opened the bowling and saw his first over disappear for 18 but recovered to take three for 97, as well as the catch for the other wicket to fall.
Chris Gayle hit the first ball of the Test for six and made 24 from 17 balls before 21-year-old Gazi had him caught by Mahmudullah at long-off.
The score moved on to 74 before Gazi then removed Darren Bravo, caught by Rubel Hossain at point.
And Marlon Samuels fell in the final over before lunch, Gazi diving forward to take the catch as Samuels pulled Shahadat Hossain's delivery to deep square leg to depart for 16.
Powell, meanwhile, was calmly building his innings, the only scare coming early when he was on seven.
Again it was Gazi causing problems as Powell mistimed his shot, edging for Rubel Hossain to catch with a dive to his left, but Powell escaped as the ball had struck the silly point's helmet on the way through.
He was 41 not out at lunch and reached his half-century with a four off Shahadat. It was only his sixth, but reaching 50 appeared to give him freedom as his next 30 runs contained another six boundaries.
Fellow left-hander Chanderpaul was playing a typically understated supporting role and took 55 balls to reach 20, but took over the bulk of the scoring duties as Powell slowed down in the 90s.
Once more, though, a boundary took the opener to his landmark as he swept Shakib Al Hasan fine to reach a 166-ball ton containing 16 fours and a six.
He greeted Shahadat's return with three successive boundaries as the partnership reached 122 by the interval, but was bowled seven balls after the restart after a swing and a miss at a ball from Gazi that kept low.
Chanderpaul's 111-ball half-century came up with his fifth four, off Shakib, and another immediately followed.
He took two boundaries in an over from the returning Rubel Hossain and Denesh Ramdin then did likewise as the scoring rate picked up, with the 50 partnership taking 69 balls.
A fortunate miscue for four took Chanderpaul to 95 and a scoreboard error led him to prematurely celebrate his hundred after another boundary. He got there off the next ball, though, with his second 50 taking just 47 balls.
Ramdin brought up his half-century in the last over of the day and the pair will resume with their partnership on 130.
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