Goran Pandev's first goals of the season came inside the opening 25 minutes to ensure Rafael Benitez's side bounced back from their shock 1-1 midweek draw with newly-promoted Sassuolo.
Genoa improved after half-time, veteran Alberto Gilardino skimming the post, but Napoli's win moved them a point clear of Roma, who could reclaim top position on Sunday when they travel to Cagliari.
In Saturday's late kick-off, Valter Birsa's goal at the start of the second half earned AC Milan a morale-boosting 1-0 win over Sampdoria.
Milan started the weekend 10 points off the league summit after just five rounds of the season and needing to make amends to their fans for their 2-1 loss to Napoli in their last match at the San Siro.
They managed to achieve that thanks to Birsa's left-footed finish in the 46th minute, but it was far from comfortable for Massimiliano Allegri's men as struggling Samp created a number of chances to draw level without managing to put the ball into the net.