Walter Mazzarri's side needed only 35 minutes to effectively wrap up the match against a team with one of the worst Serie A away records as Edinson Cavani, with a penalty, and Marek Hamsik scored.
Napoli, in third place which would earn them a place in the Champions League qualifying round, have 58 points, three more than Udinese, Inter Milan and Lazio who all play on Wednesday.
They have a fairly straightforward final two games against mid-table pair Bologna and Siena while Inter visit Lazio on the last day of the season and also face neighbours AC Milan.
AS Roma's hopes of Champions League football next season suffered another blow when they were held to a goalless draw on a rain-sodden pitch at Chievo in Tuesday's other game.
Leaders Juventus (77 points), who host Lecce on Wednesday, and second-placed AC Milan (74), at home to Atalanta the same night, have already made sure of Italy's two direct places in the Champions League group stage.
With only one away win all season, Palermo appeared to be easy prey for Napoli although they made a promising start as Josep Ilicic and Abel Hernandez forced Morgan De Sanctis to make good saves in the same move.
CONTROVERSIAL PENALTY
After Gokhan Inler hit the bar for Napoli, the hosts went ahead with a controversial penalty awarded for handball by Milan Milanovic which Palermo angrily protested was accidental.
Uruguay forward Cavani converted from the spot in the 16th minute for his 23rd Serie A goal of the season.
Goran Pandev cleverly set up Napoli's second in the 35th when, with his back to goal, he managed to hook the ball over the defence and Hamsek rolled the ball past Emiliano Viviano.
Roma have taken only two points from their last four games and their chances of finishing third and securing a place in the qualifying stage of Europe's elite competition have nose-dived.
The draw left them seventh with 52 points.
The players were forced to splash through 90 minutes of misery as driving rain left huge pools of water on the pitch.
One of the best chances fell to Chievo striker Sergio Pellissier near the end after the Roma defence failed to clear the ball, but he fired over from near the penalty spot.
