Earlier, the Caribbeans managed to score 117 runs in 52.5 overs in their second innings as Taijul Islam and Nayeem Hasan shared seven wickets and Abu Jayed took two while Mehidy bagged one.
Nkrumah Bonner (38), Joshua Da Silva (20) and John Campbell (18) were the only West Indian batsmen to reach the double-digit in the second innings.
With a handy lead of 133 from the first innings, the West Indies set a target of 231 for the hosts to level the series. But the Tigers proved that this target was also too much for them as they lost quick wickets.
It was Bangladesh's first clean sweep after the 2012-13 season. Overall, it was Bangladesh's 15th whitewash in a series with two or more matches.