Giuseppe Rossi then smashed in his second of the season soon after to double the visitors' advantage.
Genoa were able to pull one back through Alberto Gilardino early in the second half, but just 60 seconds later Rossi guided in his second to put the result beyond doubt.
Francesco Lodi then responded with his first goal for the Rossublu from the penalty spot, but that strike failed to produce a grandstand finish.
In stoppage time Genoa's defeat turned to embarrassment as they conceded a late penalty, with Mario Sampirisi dismissed for a second bookable offence.
Gomez stepped up to make it a brace from the penalty spot, turning La Viola's victory into a resounding one.