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
Shapoor Zadran named in Rashid Khan-led Afghanistan squad
Steve Smith rises to No.2 in Test rankings
PCB announce itinerary for next year's England tour
Dananjaya, Williamson reported for suspect bowling actions
Lance Klusener roped in as South Africa's assistant batting coach for India T20Is
Sri Lanka opt for three short-form games over Tests in Pakistan
Archer bags a sensational six-wicket haul with muted bouncer barrage
Mike Hesson, Simon Katich join Royal Challengers Bangalore support staff
5 ways to prevent foul play in Pakistan cricket
PSL 2019 - PSL Schedule with all PSL 4 matches and schedule for all franchises