Poli netted two thirds of the way through this contest as Bologna paid dearly for an early red card to defender Archimede Morleo.
Morleo was dismissed just five minutes into the game for a professional foul on the home side's Argentinian striker Mauro Icardi.
Despite the numerical disadvantage the visitors were the first to threaten when Alberto Gilardino shot over in the 12th minute, then two minutes later the veteran striker saw a right-footed shot from Marco Motta's cross saved by Samp goalkeeper Sergio Romero.
Sampdoria's Pedro Mba Obiang was off target twice, before Bologna's Manolo Gabbiadini shot over in the 32nd minute.
The home side's best opening of the first half came when Andrea Costa crossed for on-loan Barcelona player Icardi - but he failed to find the target from close range.
Samp started the second half on the front foot and Bologna goalkeeper Federico Agliardi did well to save Daniele Gastaldello's close-range header from Enzo Maresca's free-kick.
After Gastaldello had shot well over, Poli made the decisive breakthrough, beating Agliardi with a low shot after combining expertly with Eder.
Costa shot over 10 minutes from time, before Bologna responded with a header from Nicolo Cherubin and shot from Cristian Pasquato, neither of which threatened the home goal.
In fact, it was the home side who came closest to scoring in the closing stages through Obiang, whose shot from just outside the box went narrowly wide.