Guendouzi netted in the fifth minute on Tuesday after Luca Pellegrini won back possession and raced down the left before putting in a low cross for the France midfielder to fire into the far bottom corner.
The 24-year-old Guendouzi joined Lazio on loan from Marseille on transfer deadline day at the end of August.
Mateo Retegui came close to levelling for Genoa, including with one opportunity that had the Italy forward applauding Lazio defender Mario Gila for his block at point-blank range.
But Lazio held on and could next face Roma if Jose Mourinho’s team - who sit fourth in Serie A - can get the better of second-tier side Cremonese next month.
AAP