Mahmudullah and Nasir Hossain smashed aggressive half centuries to help guide Bangladesh to a 29-run first-innings lead over the West Indies and its highest ever test total on the fourth day of the series-opening match Friday.
Nasir scored 96 and Mahmudullah hit 62 to lead Bangladesh to 566 all out just before the scheduled lunch interval after resuming the day at 455-6.
Nasir cleared the rope four times and stroked six boundaries in a 136-ball innings that helped give the hosts a first-innings cushion in reply to the West Indies' 527-4 declared.
He was finally out, four short of his maiden test hundred, when he chased a slower ball from Timo Best and edged a low catch to Chris Gayle at slip, making the total 554-9.
The Bangladesh batting order contributed throughout the 10-hour innings, with opener Tamim Iqbal scoring 72, Naeem Islam adding 108 and Shakib Al Hasan out for 89.
Ravi Rampaul led the bowlers by taking 3-118, while Sunil Narine returned 3-148 and skipper Darren Sammy had 2-83.
At the lunch interval, the West Indies were eight without loss from four overs with Chris Gayle unbeaten on 7 and Kieran Powell on 1.