Tamim Iqbal scored his maiden Test century to help Bangladesh build a 252-run lead over the West Indies, with the tourists eyeing just their second win in Test cricket on the final day.
Bangladesh, whose only Test victory in 59 attempts came at home to Zimbabwe four years ago, reached 321 for five at the close of the fourth day, with Junaid Siddique making a smart 78.
The makeshift West Indies attack, assembled hastily after the 13 selected players boycotted the match, toiled at Arnos Vale against some accomplished batting, particularly from left-hander Iqbal.
Yet when Bangladesh tried to up the tempo in the final session, they lost four wickets and were unable to get themselves in a position to declare overnight.
West Indies stand-in skipper Floyd Reifer will be frustrated his side went through the first two sessions taking just one wicket, but his bowlers kept their discipline on a slow track.
There was early promise for the West Indies when off-spinner Ryan Austin claimed opener Imrul Kayes for 24 with the score at 82, but then Siddique joined Iqbal and the pair put on a 146-run partnership.
The 20-year-old Iqbal, reaching his first century in his 11th Test match, has frequently shown the ability to make a big score, but lacked the application to bat for long periods.
The left-hander had some good fortune, though, when he was dropped twice and his innings was spiced with attractive strokes as he looked to hit over the top.
He finally went when he smashed David Bernard for consecutive fours, but holed out to Travis Dowlin.
Siddique was caught by Dale Richards off Darren Sammy, Mohammed Ashraful was trapped leg before wicket by Kemar Roach and Sammy bowled Raqibul Hasan.
Shakib Al Hasan (26) and Mushfiqur Rahim (28) ensured a positive finish for the day for the tourist’s, who must decide just how positive they want to be with the declaration.
Against the ad-hoc West Indies, missing all their top players, they may not get a better chance for a Test win on tour for a long time.