Marlon Samuels was leading the charge for West Indies as they looked to reel in Bangladesh's first-innings 387 on day two of the second Test in Khulna.
Bangladesh added 22 to their overnight total in the morning, with debutant centurion Abul Hasan the last man out for 113, giving Fidel Edwards his sixth wicket of the second Test.
By tea the Windies had reached 146 for two, dangerman Chris Gayle and Kieran Powell the men out to leave Samuels (62 not out) and Darren Bravo (41no) in the middle.
That left the tourists 241 behind with eight wickets in hand and looking to make further inroads in the afternoon in pursuit of a whitewash in the two-match series.
Reports have suggested Hasan, who on Wednesday became only the second man in Test history to score a century on debut from number 10, had suffered a hairline fracture in a finger on his left hand.
He showed no sign of it as he drove Darren Sammy for four, but Mahmudullah was caught and bowled by the same bowler three balls later having added four singles to his overnight 72.
Hasan gloved Fidel Edwards to Sammy in the slips soon after as the seamer returned figures of six for 90.
Rubel Hossain made the first breakthrough of the Windies innings, Powell pulling a short ball straight to Shakib Al Hasan at deep square leg. Gayle (25) followed soon after, caught behind down the leg side off Sohag Gazi, as the tourists moved to 62 for two at lunch.
Samuels got things moving 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 the break 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.