Parma were competitive throughout in Genoa but were denied a battling point by Icardi's eighth league goal of the season.
The visitors looked bright on the counter throughout, with the pace of Jonathan Biabiany in particular causing problems for Sampdoria's back four.
Nenad Kristicic had the home side's first meaningful effort early in the second half with a strike from distance that was well saved.
A tight match was unlocked after 58 minutes, when Icardi profited from some poor goalkeeping and a fine cross by Marcelo Estigarribia to finish from close range.
Parma had a late chance through Amauri, but his header flashed wide and the home side held on to claim all three points.