After Tamim Iqbal's second hundred of the series and a quickfire unbeaten half-century by Mahmudullah paced the visitors to a formidable 301 for six, the hosts were restricted to 283 for six in reply despite a rampaging unbeaten 74 off just 41 balls by Rovman Powell.
It was Bangladesh's first series win outside of Asia for nine years, set up by their highest total in an ODI against the West Indies.
With the series all square following the hosts' thrilling three-run win in the second match under lights in Guyana on Wednesday, Bangladesh set the pace in this decider with their top-order batting justifying the decision by captain Mashrafe Mortaza to bat first after he won the toss for the third consecutive time.
Tamim's confident 103 off 124 balls with seven fours and two sixes again provided his team with a solid foundation, his innings lifting his tally in the three matches to 287 runs at an outstanding average of 143.5.
He was the obvious choice as both man of the match and man of the series.
"We put a lot of effort in this series after the disappointments of the Test matches," said Tamim.
"I was required to bat long and was able to do it successfully. Patience is the key to get runs on the pitches we had in this series, especially in Guyana."
As in the first two ODIs, Tamim found a reliable partner in Shakib al Hasan, the pair putting on 81 runs for the second wicket.
They picked up the pace from a stuttering start in the manner of their previous second-wicket partnerships in the series before Shakib eventually departed off the bowling off Ashley Nurse, who together with fellow spinner Devendra Bishoo put a brake on Bangladesh’s progress through the middle of the innings.
However they were able to cut loose over the final 20 overs as 150 runs were plundered in that period, thanks in the main to the unbridled aggression of Mahmudullah.
He had come to the crease when Nurse took his second wicket in bowling Mushfiqur Rahim and immediately went into attack mode, his adventurous knock of 67 not out occupying 49 deliveries and embellished with five fours and three sixes.
Tamim eventually reached his 11th ODI hundred in the 38th over but didn't get much further as a miscued sweep off Bishoo offered a catch to Powell at backward square-leg.
Big-hitting Mashrafe promoted himself up the order in a clear statement of intent, his frenetic 36 off 25 balls putting the West Indies under immense pressure during the final ten overs until his opposite number, Holder, dismissed him.
But with Mahmudullah still blazing away Bangladesh were able to cross the 300-run mark in the final over of the innings.
With a rejuvenated Chris Gayle anchoring their reply, the West Indies remained on course for the daunting target until the big left-hander fell for 73 off 66 balls, Mehidy Hasan taking the catch at long-on in Rubel Hossain's first over.
From there the innings stalled fatally as Shai Hope occupied 94 deliveries in getting to 64 and by the time he fell, with the score at 224 for five in the 44th over, the West Indies had left themselves with too much to do notwithstanding Powell's effort.
He struck four sixes and five fours in his hurricane knock but Bangladesh did not buckle under the assault with Rubel and Mustafizur retaining their disciplines in the final two overs to seal a famous match and series triumph.
"I felt 300 runs was a par score because in these conditions because it was probably the best our bowlers could do," a disappointed West Indies captain Jason Holder stated.
"We didn't progress at the rate we should have in the middle overs and left ourselves with too much to do at the end."
Both teams turn their attention to a three-match T20 series beginning in St Kitts on Tuesday and concluding at the weekend in Fort Lauderdale in the United States.
First Published: July 29, 2018, 7:59 AM IST