Asked to set a target for the third consecutive time in the tournament, West Indies posted 142 for seven with Nicholas Pooran’s 40 off 22 balls being the highlight of their innings.
The wicketkeeper batter hit four sixes and one four.
Roston Chase (39), making his T20 international debut, was the other chief contributor with the bat.
West Indies win a thriller 🔥#T20WorldCup | #WIvBAN | https://t.co/GF56PV713u https://t.co/PYfAS3YQA3
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In reply, Bangladesh could manage 139 for five in 20 overs as all West indies bowlers picked one wicket each.
With no points from three matches, Bangladesh are out of the tournament, while West Indies can still sneak into the semifinals, provided they win their remaining matches and other results go in their favour.
Bangladesh began the chase on a poor note, losing openers Mohammad Naim (17) and Shakib Al Hasan (9), who was limping, in the first six overs. But gradually picked up the momentum with wicketkeeper batter Liton Das (44 off 43) taking the initiative.
West Indies, like Bangladesh, were sloppy in the field and the two-time champions were also guilty of missing as many as three run out opportunities.
With 50 need off the last six overs with six wickets in hand, skipper Mahmudullah (31 not out) and Das looked to be in control, converting ones into twos while also hitting boundaries regularly.
Dwayne Bravo (1/36) produced a conducive 17th over, giving away just three runs. In the first ball of the penultimate over, he was hit for a six by Mahmudullah but the veteran all-rounder proved his mettle by getting rid of danger-man Das in his final ball.
Needing 13 of the last over, Mahmudullah failed to clear the boundary even once despite being dropped by substitute Andre Fletcher in the fourth ball to bring down the equation to four off the last ball.
VICTORY in a very close contest!🤯 #MenInMaroon #WIvBAN #MissionMaroon #T20WorldCup https://t.co/kfSi0PzFKF
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But Andre Russell (1/29) bowled a gem of a final delivery full outside the off stump, denying Mahmudullah any chance to free his arms to seal a close win for West Indies.
Earlier, Pooran hit four sixes and one four while Chase (39) was the other chief contributor with the bat.
Aware of West Indies struggle against spin, Bangladesh skipper Mahmudullah handed the ball to off-spinner Mahedi Hasan (2/27) to open the innings, putting pressure on the Caribbean team.
After a few overs of pace, bringing back spin in the fifth over paid immediate dividends with Hasan getting the big wicket of Chris Gayle (4) as Bangladesh gave away just 29 runs while picking two wickets in the Powerplay.
In his next over, right after he put down Chase of his bowling, Hasan snared Shimron Hetmyer’s (9) wicket.
Kieron Pollard (14 not out) and Chase tried to repair the innings before the skipper retired ill in the 13th over.
The reasons for his walking out at that stage were not clear but he came back in the final over to hit a last ball six after seven batter of his side were packed off.
In the very next ball, Andre Russell (0) was run out without facing a ball as things went from bad to worse for the West Indies.
Then on West Indies got some rub of the green when Chase was dropped once again by Hasan at deep mid-wicket before Bangladesh missed a stumping opportunity against Pooran.
The momentum slightly changed in the West Indies favour as Chase and Pooran plundered 14 runs off the 15th over.
Pooran continued the assault as he hammered Shakib Al Hasan for back-to-back sixes.
Jason Holder too pitched in with an unbeaten five-ball 15.