Pooran found some support from Keacy Carty (33) and Rovman Powell (18) but failure from the top order once again hurt the Caribbean side.
Earlier, Bangladesh picked just one pacer in Mustafizur Rahman for the match as they dropped left-arm pacer Shoriful Islam for left-arm spinner Taijul Islam.
Taijul justified his inclusion by striking in his very first ball of the match, rattling the stumps of opener Brandon King (eight).
In his following over, he dismissed the other opener Shai Hope for two with wicketkeeper Nurul Islam completing the stumping.
The following over, Mustafiz trapped Shamrh Brooks lbw for four to reduce the hosts to 16-3 inside six overs.
West Indies then fought back on the back of a 67-run fourth wicket stand between Pooran and Carty.
Just when it looked like the hosts are setting a base for a late assault, Carty threw away his wicket by giving a simple catch to Tamim Iqbal off Nasum Ahmed to depart for 33.
Powell and Pooran then added 34 runs for the fifth wicket before Taijul once again came to the party, bowling the former to reduce them to 117-5.
Running out of partners, Pooran decided to begin his counter-attack, smashing 16 runs of Mehidy Hasan Miraz in an over and helping his team to breach the 150-run mark.
But Taijul removed Pooran in his final over of the match and crushed West Indies’ hopes of reaching the 200-run mark.
Romario Shephard's 19 off 21 balls pushed the total closer to the 200-mark before Nasum went through his defences to end the innings.
Earlier, Tamim won the toss for the third straight time in the ODI series and for the third time opted to bowl first.
Bangladesh is playing an ODI with a one-man pace attack after almost 10 years.
Bangladesh have won the previous 10 ODIs they have played against West Indies and have a chance to extend the number to 11.
The Tigers already have the series in the bag as they lead the three-match series 2-0.