West Indies started the day 167 runs behind Bangladesh and finished it 106 runs ahead in the second test at Daren Sammy Stadium on Saturday.
Allrounder Kyle Mayers led the turnaround with a chanceless and unbeaten 126 runs, easily the highest score by either side after two days.
In reply to Bangladesh’s sub-par 234, West Indies moved from 67 without loss overnight to 340-5 at stumps.
Winner of the first test in Antigua in just over three days, West Indies was well on course to clinch the short series.
After captain Kraigg Brathwaite scored 51 and contributed a century opening stand with John Campbell, Mayers stopped a mini-collapse with Jermaine Blackwood, and cruised on with Joshua Da Silva.
Da Silva was 26 not out after facing 106 balls.