Sampdoria, having won only one of the last six derbies, were out to take early control, and they did just that when Andrea Poli turned in a deflected shot from 12 yards after 16 minutes.
Genoa were desperately unfortunate to concede a second when goalkeeper Sebastien Frey saved Mauro Icardi's drive at the near post, only for the ball to ricochet onto team-mate Cesare Bovo and into the net from six metres before the break.
Icardi came close to netting again before the break but was too isolated to convert Nenad Krsticic's pass in stoppage-time.
Bovo took the bench for the second half off, with Juan Manuel Vargas taking his place while Andrea Bertolacci replaced Daniel Tozser in midfield.
Ciro Immobile took one back for Genoa in the 73rd minute via a goal in a packed penalty area, before Serie A debutant Icardi made good of his first-half promise, finally scoring two minutes from time to restore Sampdoria's two-goal lead.
Genoa's sixth defeat in a row left them bottom with nine points, while Sampdoria climbed to 14th with 13 points.