Genoa started the match confidently with a three-man attack and took the lead after 22 minutes through Gilardino, who turned home Giovanni Marchese's cross.
© Getty Images
Chievo struggled to respond but looked a different side in the second half, levelling thanks to clinical counter shortly after the interval.
Simone Bentivoglio crashed home off the crossbar to equalise, but their parity lasted for just two minutes as Genoa managed to retake the lead in bizarre circumstances.
Gilardino was the man to profit after being hit full in the face by Bentivoglio's goal-line clearance, which went over the line to put Gian Piero Gasperini's troops back in control.
The Flying Donkeys threw on Perparim Hetemaj and Cyril Thereau in search of an equaliser, but were unable to profit from seven added minutes as Gasperini's men held on for only their second victory of the campaign.