West Indies also won the preceding two-match Test series by seven and 10 wickets respectively against Bangladesh.
Captain Nicholas Pooran came down the pitch and smashed Bangladesh counterpart Mahmudullah over the fence to complete West Indies' T20 win and series sweep. Pooran's career-best 74 not out off 39 balls finished off Bangladesh by five wickets with 10 balls remaining.
Both the sides made one change each. The Windies brought in Dominic Drakes for Keemo Paul, while the visitors have Nasum Ahmed in for Taskin Ahmed.
West Indies scored 169-5 in reply to Bangladesh's 163-5 in the third T20 to win the series 2-0. The first match in Dominica last weekend was washed out. Bangladesh chose to bat first, and a 20-run over plundered off Odean Smith by Litton Das and Afif Hossain gave the visitors a big boost.
Their 57-run stand ended when Litton charged Hayden Walsh and edged to point. Liton made 49 off 41 balls. In the 19th over, Walsh trapped Mahmudullah on 22 and Afif was run out on 50 off 38 balls. He'd hit only two boundaries and two sixes in his second T20 fifty.
Chasing 164 to win, West Indies overcame a spin-heavy attack from Bangladesh. Opener Kyle Mayers got going to his 55 from 38 balls when he blasted his first six off Nasum Ahmed over long off. He linked with Pooran at 43-3 in the seventh over, and they combined for 85 in 8.3 overs.
Mayers launched sixes against Shoriful Islam, Mustafizur Rahman and Mosaddek Hossain, one of them into the sight screen. He earned his maiden T20 fifty. In the same 15th over Mayers was out to Nasum, Pooran hit two sixes. The over went for 19 runs.
Pooran maintained the onslaught — his ninth T20 fifty — by hitting Afif over long off in the 18th over and his fifth and final six back over Mahmudullah's head to end the series. The teams stay in Georgetown for three one-day internationals starting on Sunday.
West Indies: Brandon King, Kyle Mayers, Shamarh Brooks, Nicholas Pooran (c & wk), Rovman Powell, Romario Shepherd, Odean Smith, Dominic Drakes, Akeal Hosein, Obed McCoy, Hayden Walsh.
Bangladesh: Anamul Haque, Litton Das, Shakib Al Hasan, Mahmudullah (c), Afif Hossain, Nurul Hasan (wk), Mosaddek Hossain, Mahedi Hasan, Nasum Ahmed, Shoriful Islam, Mustafizur Rahman.
The Windies also won the preceding two-match Test series by seven and 10 wickets respectively. The two teams will also play a three-match ODI series in Guyana, starting Sunday (July 10). Bangladesh's tour of West Indies 2022 concludes on July 16 with the third and final ODI.