The West Indies started their first innings of the Lucia Test 234 runs behind Bangladesh and finished it 174 runs ahead at the Daren Sammy Stadium Sunday.
Kyle Mayers' epic knock of 146 came to an end as he fell to Khaled Ahmed on day three. It was Khaled's fourth wicket in the innings.
Bangladesh picked up two wickets in the first session of the day before the rain came in.
In the rain-hit first session, the West Indies added 36 runs with their overnight total of 340 for five and lost two more wickets.
The hosts had lost four wickets for 132 runs. But Mayers, Jermaine Blackwood and Joshua Da Silva stood firm to strike back and secure a first-innings lead for the hosts.
Earlier, Bangladesh scored 234 in the first innings with only a 50 from Liton Das. All of Bangladesh's first five batters managed to have good starts, but they failed to carry on.
At the end of day two, Bangladesh's head coach Russell Domingo had said the batters should learn from the West Indies.
The hosts won the first Test of the ongoing series, which is a part of the ICC World Test Championship.