Jose Callejon opened the scoring after 15 minutes and the lead was doubled five minutes later as Marek Hamsik found the target.
Lucas Castro reduced the deficit in the 25th minute but Napoli dominated the remainder of the game and the visitors were lucky to lose by just a single goal.
Gonzalo Higuain saw a header come back off the bar as Napoli asserted their control in the early stages and five minutes later they were ahead with a stunner from Callejon.
The former Real Madrid man let fly with a left-foot shot which Mariano Andujar had no chance of stopping.
The lead was nearly doubled as some impressive build-up play from Callejon, Hamsik and Higuain allowed the Argentinian to force Andujar into an impressive save.
And just a minute later they did have another through Hamsik.
Lorenzo Insigne found the Slovakia international and his effort from inside the box nestled in the bottom right corner.
Napoli had been rampant but 20 minutes before half-time Catania had an equaliser against the run of play when Castro's half-volley beat Jose Reina.
Sergio Almiron fired over the bar as the visitors briefly had their tails up but it was all Napoli from that point onwards with Hamsik bringing a further save from Andujar before half-time.
Higuain had two good chances saved by Andujar after the break as Napoli pressed but the Argentinian keeper produced his best work to claw away Raul Albiol's close-range header.
Higuain and Callejon both had further chances to extend the lead but could not find the target while Pablo Armero and Dries Mertens also tried their luck as the clock ticked down.