Shakib and Mushfiqur Rahim finished the remaining job for the hosts. Both Shakib and Mushfiqur remained unbeaten for 43 and 9 respectively.
Mehidy was awarded the man of the match for taking four wickets for 25 runs.
Earlier, the West Indies could not overcome their poor batting show and were wrapped up for only 148 for all in the second game of the ODI series.
Right-arm spinner Mehidy Hasan Miraz bagged four for 25 in 9.4 overs, his best bowling figure in ODI. His previous best was taking four for 29 runs. Mustafizur Rahman and Shakib Al Hasan took two wickets each.
Unlike the first match of the series, Jason Mohammed, the stand-in captain of the West Indies, won the toss and opted to bat first. His decision came as a surprise as the wicket, which was used in the first game as well, was not a good one for the batsmen.
However, the West Indies did not lose their first wicket in the second over as they did in the first game. Despite that, they failed to take control of the game with the bat.
Mustafizur brought the first breakthrough for the hosts, removing Sunil Ambris in the fifth over for 6. The debutant Kjorn Ottley and wicketkeeper-batsman Joshua Da Silva faced 50 balls in the second wicket stand to post only 26 runs.
Mehidy took the second wicket removing the debutant Ottley for 24. It was a length ball at the outside off stump. And Ottley hit the ball hard only to be caught by Tamim Iqbal at the extra cover area.
And the right-arm spinner took the next wicket as well, dismissing Joshua Da Silva for 5 off 22 balls. This time it was a length ball again, and Da Silva defended, thinking the ball was coming into him. But the ball was straight and dislodged his stumps.
When the West Indies were struggling at 37 for three, Shakib bowled Ande McCarthy out for three and Najmul Hossain Shanto displayed a wonderful fielding effort to trap Kyle Mayers run-out for a duck.
In the sixth wicket stand, Mohammed and Nkrumah Bonner added 26 runs. When the partnership was getting big, Hasan Mahmud came to the scene and removed Booner for 20 off 25.