Marek Hamsik added the third five minutes later. Fabrizio Miccoli grabbed a consolation for Palermo three minutes from time.
Bologna are now six points clear of the drop zone after beating 10-man Catania 2-0.
Nicolo Cherubin scored five minutes into the second half and captain Marco Di Vaio doubled Bologna’s lead in stoppage-time. Catania captain Marco Biagianti was dismissed in the 77th minute for a second yellow card.
Pasquale Marino replaced Alberto Malesani on the Genoa bench at the start of the break, but his side got off to a dreadful start, losing 3-0 at Cagliari.
Joaquin Larrivey fired Cagliari in front in the 13th minute from the spot and Victor Ibarbo doubled their lead after the break, before Genoa fell apart as defender Emiliano Moretti was dismissed in the 66th minute and Andreas Granqvist turned the ball into his own net six minutes later.
Elsewhere, AS Roma captain Francesco Totti scored two penalties to help his side to a 2-0 win over Chievo Verona and Stevan Jovetic also scored twice — including once from the spot — as Fiorentina beat struggling Novara Calcio 3-0.
Riccardo Montolivo grabbed the Tuscan side’s other goal.