After a two-hour rain delay at the start of the day, Bangladesh took just 4.1 overs to take the last two West Indies wickets and bowl them out for 209.
Bangladesh reached 17 for 0 by lunch and they now have five sessions, weather permitting, to chase the target and wrap up a historic series win in West Indies.
David Bernard, who had resisted for an unbeaten 61 on day three, added nine to his overnight score, that included a six, before he was stumped as he stepped out to lift a fuller delivery on middle and off from Enamul ul Haq jnr. Tino Best too hit a big six over long off against Shakib Al Hasan before he gloved an attempted sweep to the keeper.
It was the first time Bangladesh had bowled out the opposition for less than 250 in both innings. Bangladesh have had some problems against the seamers and it would be interesting to see how they go about their task.