Bangladesh were 164-3 at close on the second day in reply to the mammoth West Indian total of 527-4 declared in the first Test in Dhaka on Wednesday.
Naeem Islam was unbeaten on 27 and with him Shakib Al Hasan on 16 as the home team still needed 164 runs to avoid the follow-on.
Shivnarine Chanderpaul scored 203 not out to equal his highest Test score while Denesh Ramdin made 126 not out in the visitors' innings.
The 38-year-old left-hander batted with composure to equal his highest Test score of 203 not out as the touring batsmen dominated a hapless Bangladesh bowling attack before captain Darren Sammy declared at the tea break.
Denesh Ramdin, who remained not out on 126 for his third Test hundred, ably supported his partner as the pair added 296 for the fifth wicket stand -- a new record in all West Indies-Bangladesh series.
Chanderpaul drove spinner Sohag Gazi towards point for two to complete his double ton off 367 balls which had 22 boundaries. He had also scored 203 not out against South Africa at Georgetown in 2005.
He took his helmet off to acknowledge the cheers from a small crowd and team-mates before bending down to kiss the ground. In all he batted for 457 minutes, faced 372 balls and hit 22 fours.
Chanderpaul's stand with Ramdin beat the previous best of 262, incidentally involving him and Ramnaresh Sarwan at Kingston eight years ago.
Both frustrated the Bangladesh bowling in the two sessions after the West Indies resumed at their overnight score of 361-4, looking to bat out their opponents in the first of two Tests.
Ramdin, 52 overnight, looked unperturbed in the company of his illustrious partner, reaching his century with a boundary and a flick for two off spinner Shakib Al Hasan. He took 208 balls and hit nine boundaries in the milestone.
He hit 11 boundaries and a six.
Debutant Gazi was the pick of bowlers with 3-145. Paceman Shahdat Hossain took the other wicket.