He is playing his first tournament since suffering serious injuries in a car accident in December 2022 that kept him out of last year's IPL as well as the 50-overs World Cup in India
Tamim smashed his way to strike 103 off 124 balls with seven boundaries and two sixes.
West Indies need to score 302 to win the three-match series against visitors.
Earlier, Bangladesh have won the toss and opted to bat first.
On Jul 22, the visitors beat the hosts by 48 runs in the first ODI at Guyana’s National Stadium.
In the second game played at the same venue on Jul 25, Bangladesh lost by just three runs to Windies.