Rodrigo Palacio was on target twice with Alberto Gilardino opening his account for Genoa, who led 3-0 with nine minutes remaining.
However, goals from Edinson Cavani and Ezequiel Lavezzi within the space of a minute gave the visitors hope as they threatened an extraordinary comeback, just falling short as they ran out of time.
Palacio had a good chance to put Genoa ahead in the 14th minute when he shot over the crossbar from eight yards out.
It was certainly more of a chance than the one he actually took to put Genoa in front in the 31st minute, volleying the ball unstoppably past Morgan de Sanctis from 25 yards.
Five minutes later and Gilardino made it two for the home team with his first goal for the club.
Giuseppe Sculli lifted the ball into area and Gilardino headed it in from six yards with De Sanctis getting a hand to the ball, but only lifting it into the roof of his goal.
Napoli coach Walter Mazzarri resisted the temptation of bringing Cavani on at the start of the second half and perhaps he waited a little too long.
Palacio missed the chance to add a third in the 51st minute when he intercepted a weak pass by Blerim Dzemaili in the centre of the field, but he got the ball caught between his feet and wasted what was a clear route to goal.
Marek Hamsik finally found an opening at the other end, but Sebastien Frey thwarted him with a good save.
Palacio then gave Genoa a bit of security with the third goal in the 70th minute.
Gilardino played the ball into his path and he only needed to set himself up and shoot into the far corner with one touch.
Cavani was now on the field and he gave Napoli some hope in the 81st minute when he headed in Cristian Maggio's cross.
Less than 60 seconds later, Lavezzi had the ball in the back of the net again as he held off Giandomenico Mesto to fire into the top corner, reopening the game inside the last 10 minutes.
Napoli searched for an equaliser, but Genoa held firm for their second successive 3-2 win at home having defeated Udinese by the same scoreline a fortnight ago.