Having dominated the early proceedings, hosting Samp eventually broke the deadlock with 33 minutes played.
Pedro Mba Obiang picked out Poli inside the area and the midfielder slotted the ball into the bottom right hand corner of the net.
The home side continued to control proceedings after the restart, but it wasn't until seven minutes from time that they secured the victory.
A quick counter-attack ended when Shkodran Mustafi found Eder, who in turn fired into the net from close range.
The result has moved Samp up to 10th in the Serie A standings, while visiting Chievo remain 13th.