Mushfiqur Rahim helped the Tigers overhaul the paltry 195-run total of the tourists with a half- century after captain Mashrafe Bin Mortaza led the bowlers to restrict the Caribbean batsmen at the Mirpur Sher-e-Bangla National Cricket Stadium on Sunday.
It was not a good day for Imrul Kayes (4) and Soumya Sarker (19) either.
Shakib Al Hasan contributed with a 30-run knock while Mahmudullah remained unbeaten on 14.
Earlier, Mashrafe helped the Tigers run through the West Indies top order.
He struck after Shakib took out opener Kieran Powell (10) in the eighth over.
The skipper broke the steady opening stand when he snared the wicket of Darren Bravo in the 21st over. Tamim sprinted and dived to take a fine catch.
He also returned the best bowling figures of 3-30 in his 10 overs.
Few West Indies batsmen looked comfortable at the crease.
Roston Chase contributed 32 and Keemo Paul made 36 to take the West Indies close to the 200-mark before Mustafizur hit late, taking 3 for 35.
Besides Shakib, Mehidy Hasan Miraz and Rubel Hossain each picked up one wicket.
The West Indies had won the toss and chosen to bat first.