Alberto Paloschi scored the only goal of the game at the Stadio Marc'Antonio Bentegodi and also missed a penalty.
Paloschi latched on to a clever flick-on from Riccardo Meggiorini and netted with a composed low finish in the 35th minute.
The striker was then afforded a golden opportunity to double his tally in the 62nd minute as Sinisa Andelkovic handled in the area, but Paloschi sliced the resulting spot-kick over the crossbar.
Franco Vazquez smashed the bar from 10 yards out late on for Palermo before Andelkovic was sent off for a second yellow card with four minutes remaining as Chievo moved 11 points clear of the drop zone.
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