The Bangladeshis were not required to break any records to seal their victory in this do-or-die encounter.
Shakib has now scored two centuries at the World Cup after hitting 121 against England.
Bangladesh's joint highest one-day worldwide run chase put them behind only Ireland's 329-7 against England in 2011 in the history of successful World Cup chases.
Earlier, Hope missed out on a hundred as the West Indies failed to capitalise on a good start to post 321/8 in 50 overs. But I keep on saying one thing - that at least four more matches left and it's the midway of the tournament.
Tasked with being the glue that holds an otherwise powerful West Indies together, the wicketkeeper-batsmen narrowly missed out on his century, falling to the bowling of Mustafizur Rahman on 96. But he left the field after bowling three overs, and after six overs, and was a reluctant fielder while hobbling around.
A day after skipper Mashrafee bin Murtaza slammed the team management for judging the wicket by listening to commentary Sakib al Hasan found a positive side of it.
Liton, however, believed that Bangladesh are in a much better place to face the Australians after comfortably handling West Indies' short balls in Taunton. Each time he's batted, Shakib has reached 50.
Shakib was fortunate not to be caught on two occasions in successive overs. When he was scoring I felt really good, and when I was scoring he also felt really good because when I scored my fifty he came running towards me and gave me a hug.
Andre Russell is playing for West Indies, which made only one change - Darren Bravo is in for Carlos Brathwaite to shore up the batting after missing out on the loss to England last Friday. Tamim was run out for 48, Sarkar fell for 29 and Mushfiqur fell for 1 run, bringing out Liton Das to the pitch to partner Shakib, who is in a purple patch with the bat at the moment.
As bowler, though, like his team-mates, Cottrell could make little impression from 22 yards away. He had not played an global match for Bangladesh since May 15, when he made 76 off 67 balls opening the innings against Ireland.
A 13-ball duck was the second of Gayle's World Cup career, both against Bangladesh. His opening five-over spell from the River End was the longest of any bowler. We've got to come back stronger.
At 143 for 3 in the 22nd over, Shakib tried to swing Thomas over the leg-side and sent a skier down towards Shannon Gabriel on the fine-leg boundary.
Shakib said: "I told Liton that if you stay at the wicket then we can finish this game with three wickets down and after 10 or 15 balls, it was a treat to watch".
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