The Genoa-based team needed a win to survive until the final round of matches, but the loss combined with Lecce’s 2-0 victory over Bari means Sampdoria is four points behind Lecce.
Bari and Brescia were already relegated.
Sampdoria forward Nicola Pozzi found the net in the 30th minute but the strike was ruled out, seemingly wrongly, for offside, and Palermo captain Fabio Miccoli took advantage of the let off by giving Palermo the lead in first half injury time.
Jonathan Biabiany gave Sampdoria some hope early in the second half, but Mauricio Pinilla scored the winner four minutes from time.
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