Paul posted the best-ever T20 figures for a West Indies bowler to help the visitors bowl out Bangladesh for 140 runs.
Shakib smacked 42 off 26 balls to help Bangladesh post 211/4 before taking his maiden five-wicket haul to script a 36-run victory
Shakib now has two demerit points, having been handed one for an offence during a Twenty20 against Sri Lanka in March this year.
West Indies raced to 130-2 in just 10.5 overs after Cottrell and his fellow pacers bowled out Bangladesh for 129 runs in Sylhet.
The first T20 will be played on Monday at the Sylhet International Cricket Stadium, while Dhaka will host the next two matches on December 20 and 22
Tamim Iqbal and Soumya Sarkar slammed half-centuries as Bangladesh cruised to an eight-wicket win over the West Indies
Saifuddin and Mithun replaced Mosaddek Hossain and Sabbir Rahman, who played in Bangladesh's last T20 series against the West Indies in July-August
The Caribbean side last won an ODI series in 2014 at home against Bangladesh and are desperate to end the drought
Hope smashed a brilliant century as West Indies edged Bangladesh by four wickets in the second one-day international
Wobbly England pit against bitter rivals Australia
Rabada: South Africa must learn 'painful' lessons from their World Cup campaign
Brampton Wolves: the latest entrant in GT20 Canada
Wasim Akram highlights Shaheen Afridi’s significance
Highlights: Hafeez pumped up after Pakistan victory
Haris Sohail returns to the side with a bang
The culture of trolling players on social media needs to change: Waqar Younis
Babar Azam not satisfied with his World Cup so far
If England claim to be the best, now is the time to prove it
Joe Burns diagnosed with burn-out depleting his chances of Ashes selection