Visiting Sampdoria went ahead in the 18th minute when Genoa failed to clear a through ball from Cassano and Roberto Soriano nipped in to score.
Cassano was also involved in the second goal that came when Brazilian-born Eder shot past goalkeeper Mattia Perin six minutes before the interval to claim his 11th league goal of the season.
Sampdoria then surged into a 3-0 lead in the 49th minute after Cassano laid the ball on for Soriano and he drove it home left-footed.
Genoa refused to lie down, though, and Leonardo Pavoletti gave them hope when he headed in a corner after 69 minutes.
Pavoletti nodded his second goal 11 minutes later to set up a frantic finish but Sampdoria held on for a victory that pushed them up to 11th in the table with 23 points from 18 matches.
Genoa remained fourth from bottom with 16 points, two points above the relegation zone.
(Writing by Tony Jimenez; Editing by Justin Palmer)
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