Seeking a third successive victory on the road for the first time since November 2023, the visitors were millimetres away from taking the lead after just five minutes as Romelu Lukaku’s header beat Nicola Leali but not the underside of the crossbar.
In response, only a last-ditch interception from Rrahmani prevented Vitinha’s effort from finding the back of the net.
However, the game’s opening goal came in the next attack, with David Neres’ delightful delivery into the danger zone headed home by Anguissa to give the visitors a 15th-minute lead.
Matters got worse for Genoa eight minutes later as Rrahmani glanced home his first goal of the season from Stanislav Lobotka’s inswinging set-piece to put Napoli in complete control of proceedings.
Scott McTominay then had a goal ruled out for an offside ahead of the break, which would have capped off an excellent first half for Antonio Conte’s visiting side.
In need of a much-improved performance in the second period, Genoa needed less than six minutes to halve the deficit. Vitinha’s mesmeric wing-play put the ball on a plate for top-scorer Andrea Pinamonti to take a touch in the centre of the area before sublimely slotting the ball past Alex Meret into the far corner.
Milan Badelj’s towering header called Napoli’s shot-stopper into preserving their slender lead not long after, as the hosts continued their push for an equaliser.
However, despite the one-way traffic, which saw substitute Mario Balotelli hit the post, Genoa were left empty-handed as a fourth win from their last five league matches gives Napoli every chance of being atop the Serie A tree at Christmas should Atalanta lose to Empoli tomorrow.
Conversely, Genoa remain two points above the bottom three after failing again to register their first home victory this season (D6, L4).