After losing the momentum on the opening day thanks to a stunning hundred from Tigers debutant tailender Abul Hasan, the tourists wrapped up the first innings for 387 and then posted 241 for two in reply.
Samuels' 109 not out from 231 deliveries was the centrepiece, with Darren Bravo finishing 85 not out having shared in a 198-run third-wicket stand. That total leaves the Windies 146 short with plenty of time to build a lead.
Bangladesh added 22 runs to their overnight 365 for eight, with Hasan showing no noticeable signs of a reported fractured finger. Mahmudullah was dismissed for 76 by Darren Sammy before Hasan handed Fidel Edwards his sixth success of the innings to go for a memorable 113.
The Windies' innings started rapidly, Rubel Hossain making the first breakthrough, Kieran Powell pulling a short ball straight to Shakib Al Hasan at deep square leg.
Dangerman Gayle, who hit a six off the first ball of the match last time out, followed for 25 soon after, caught behind down the leg side off Sohag Gazi, as the tourists moved to 62 for two at lunch. But Bravo and Samuels proved tougher to remove than the opening pair.
Samuels got things moving in the afternoon with a four and a six off successive Shakib deliveries in the 36th over and hit his third and fourth boundaries off Rubel 10 overs later. That saw him to his half-century from 107 balls and by tea he was 62 off 126 balls.
Bravo was in less of a hurry at the other end and by tea had hit just two fours in 115 balls at the crease. The pair also stayed together for a second full session, moving the score along from 146 to 241 by stumps.
Bravo's 50 came in 133 balls with a swept boundary off Mahmudullah but there were few real fireworks as the Windies pair dug in diligently to work ones and twos for most of the evening's play.
Boundaries were relatively few and far between but Samuels flashed the 11th of his innings through cover to reach three figures from the last ball of the 80th over. Just two more were bowled, with Samuels striking the penultimate ball of the day for four more.