Goals from Goran Pandev and Blerim Dzemaili in the first half earned Walter Mazzarri's side all three points at the Stadio San Paolo with Edinson Cavani seeing his penalty saved in the second half.
A third goal was not required to assert Napoli's authority on the game, though, as they reduced the arrears on Juventus to nine points with seven games of the season left, but perhaps more importantly increased their advantage over the Rossoneri.
Genoa, meanwhile, are in 18th place with relegation becoming an increasingly serious prospect.
It could have been a completely different night for Genoa had Bertolacci's second-minute effort not been saved by Morgan De Sanctis.
The visitors looked motivated, but the wind was taken from their sails in the 18th minute when Cavani played in Pandev, who skipped past Emiliano Moretti as he slipped and lifted his shot into the top left-hand corner.
Dzemaili doubled Napoli's advantage just 10 minutes later when he was set up by Marek Hamsik, coolly slotting the ball into the far corner beyond the reach of goalkeeper Sebastien Frey.
Napoli had the chance to make it three midway through the second half when Jiraj Kucka clipped the heel of Hamsik inside the area, but Frey pushed Cavani's penalty away to safety.
The Frenchman proved to be Cavani's nemesis as he made two more fine reflex saves from the Uruguayan striker, who confirmed it was not his night when he blazed a shot wide with the goal gaping in the last minute.