© Getty Images
They came close again minutes later as Blerim Dzemaili forced the keeper to beat away his powerful free kick.
Napoli added a second in the 25th minute after Andujar spilled a long ball and Callejon was on hand to tap home from inside the box.
Catania almost responded immediately through Keko, who smashed a strike from the edge of the area against the bar.
The visitors were in complete control and scored a third in the 40th minute, when Henrique fired a powerful half-volley into the top corner from a tight angle.
They added a fourth with two minutes of the half left to play as Zapata was played in by Callejon, and he kept his composure to calmly slot the ball past the keeper.
They scored a second in the 75th minute when Norbert Gyomber headed in a corner, but Napoli managed to hold on and claim the three points.