The Serie B side beat their Serie A opponents despite having Fabrizio Cacciatore sent-off in the 68th minute when the score was still 1-1.
Luigi Giorgi gave Palermo the lead after just seven minutes but Verona went right up the other end and scored through Andrea Cocco.
Cacciatore's second booking looked to hurt Verona but Chilean defender Carlos Labrin then needlessly put into his own net in the 72th minute.
Palermo were wasteful in possession and in front of goal all night and Verona hung on for the victory.
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