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.
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.
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.
