- Mattia Bani (40')
- Mateo Retegui (56')
- Giacomo Raspadori (76')
- Matteo Politano (84')
Napoli provisionally moved up to fifth in the standings with seven points from four games.
Genoa, who returned to Serie A after being relegated in 2021-22, defended well against visiting champions and defender Mattia Bani earned the lead in the 40th minute, sending the ball into the roof of the net following a corner.
Napoli were helpless in front of goal and Khvicha Kvaratskhelia sent their first shot on target in the 72nd minute but his low effort towards the left corner was easily denied by Genoa keeper Josep Martínez.
But Raspadori gave Napoli hope of a comeback shortly after when he narrowed the deficit with a shot into the top corner.
Encouraged by the goal, Napoli pushed for an equaliser and substitute Politano levelled with a close-range volley six minutes from time, denying Genoa a second win of the season.
"Mine was an important goal but it wasn't enough, we had to win and there is regret because we created many opportunities without managing to materialize them," Politano told Sky Sport.
"We can't afford any more mistakes. From tomorrow morning we'll think about the Champions League."
Genoa, who are 12th on four points, will travel to Lecce on Friday.
- Michael Fabbri