Frank Anguissa and Amir Rrahmani found the net for Napoli within an eight-minute span during the first half, but Andrea Pinamonti reduced the deficit shortly after the break.
Genoa dominated significant portions of the match thereafter, with Mario Balotelli missing a crucial chance to equalize in the 85th minute.
Napoli now holds 38 points, leading Atalanta by one point, who have the opportunity to reclaim the top spot on Sunday as they seek their 11th consecutive win at home against Empoli.