Roma were held to a 1-1 draw by relegation-threatened Atalanta earlier on Sunday as Francesco Totti's third-minute penalty was cancelled out by German Denis' spot-kick to move the visitors seven points clear of the drop.
And Rafael Benitez's men duly took advantage as they cruised to a comfortable victory in Sardinia to leave Cagliari nine points adrift of safety.
Jose Callejon's cool 24th-minute strike gave Napoli the lead, which was doubled on the stroke of half-time by an Antonio Balzano own goal.
Manolo Gabbiadini's curler then put the game beyond Cagliari's reach, despite Napoli midfielder Christian Maggio being given his marching orders for a second yellow card in the 65th minute.
Financially-stricken Parma could be relegated next week after a 2-2 draw at Empoli. Ishak Belfodil secured a share of the spoils for the bottom club after Massimo Maccarone and Lorenzo Tonelli had put Empoli ahead following Francesco Lodi's opener.
Elsewhere, a double from Ivaylo Chochev gave Palermo a 2-1 success over Genoa, Sassuolo drew 1-1 with Torino and Chievo were held to a 1-1 stalemate by Udinese.
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