Earlier, Bangladesh made short work of the West Indies middle-lower and lower order to bundle out the visitor for 259 and secure a 171-run lead.
The Tigers’ spinners bagged the last five Caribbean wickets at the expense of just six runs, with Mehidy Hasan Miraz (4-58) earning three of those scalps.
Jermaine Blackwood (68) and Joshua Da Silva (42) added 99 runs in a sixth-wicket recovery stand to push their team past the follow-on threshold in their chase of Bangladesh’s daunting 1st innings total of 430.
West Indies added 114 runs after losing three wickets while Bangladesh floundered four dismissal opportunities in the first session.
Left-arm spinner Taijul Islam gave Bangladesh the perfect start to the day dismissing Nkrumah Bonner (17) with the first ball of the day.
However, Bangladesh bowlers became wayward as the overs rolled and gave away scoring opportunities to the batsmen even though the pitch offered more turn than the first two days.
The batsmen smashed 18 boundaries and a six in the first session, mostly of poor deliveries. Skipper Kraigg Brathwaite (76) added 55 runs with debutant Kyle Mayers (40) before Nayeem Hasan gave the breakthrough.
Centurion from the previous day Mehidy Hasan Miraz soon sent Mayers packing by trapping him in front to leave the West Indies on 154 for five.
Two of the four reprieves were given by wicketkeeper Liton Das while substitute fielder Yasir Ali Chowdhury dropped two catches at short leg.