Bangladesh were struggling at 105-4 at stumps of day two in their must-win second Test on Friday, after the West Indies scored 409 runs in the first innings.
Mushfiqur Rahim was batting on 27 alongside Mohammad Mithun, six not out, at the close.
Shannon Gabriel picked up 2-31 for the West Indies.
Earlier, Joshua Da Silva was the highest scorer for the visitors in their first innings, with 92 runs, while Nkrumah Bonner and Alzarri Joseph added 90 and 82 runs respectively.
Abu Jayed (4-98) and Taijul Islam (4-108) were the most successful bowlers for Bangladesh.
The visitors won the first Test in Chittagong by three wickets in sensational fashion, making 395-7 in the fourth innings - the fifth-highest successful run chase in the 144-year history of Test cricket.