Set an improbable target of 489 after the home side declared their second innings at 269 for four, 45 minutes into the day, the tourists crashed from 158 for two to be dismissed for 192 just before a shower swept across the ground.
Opening batsman Tamim Iqbal (64) and Mominul Haque (56) held up the West Indies for over three hours with a second-wicket partnership of 110, but when Tamim skied an attempted sweep off Benn to midwicket it was the trigger for the collapse.
It was completed when Kemar Roach breached the defence of Shafiul Islam to set off the West Indies victory celebrations in their 500th Test and a 2-0 sweep of the series.
"This is unbelievable," said an overjoyed West Indies captain Denesh Ramdin, who waited until senior batsman Shivnarine Chanderpaul completed his 30th Test hundred in the morning before declaring.
"It's a wonderful feeling but we know that there are greater challenges ahead."
Captain Mushfiqur Rahim was the last hope for Bangladesh taking the match into the fifth day after Tamim and Mominul departed.
However he was bowled for the second time in the match, falling to Taylor who then promptly trapped Robiul Islam leg-before to become the 20th West Indian to claim 100 wickets in Test cricket.
"We showed some resistance for a while but that's not good enough," said a crestfallen Mushfiqur.
"We need to play better for longer periods if we want to be competitive going forwards," he said.

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