In spite of losing two wickets for 36 runs in the session, West Indies are in the driving seat, as they extended their lead to 142.
Earlier, the hosts resumed the day’s play on 340-5, leading by 106 runs.
Bangladesh got the first breakthrough of the day in just the second over when Miraz trapped Da Silva lbw for 29 to break the 96-run stand.
Alzarri Joseph pulled a short ball from Khaled straight to Liton Das to depart for seven as West Indies got reduced to 363-7.
Mayers was then joined by Roach and the two added 13 runs for the eighth wicket before rain halted play.