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They came close again minutes later as Blerim Dzemaili forced the keeper to beat away his powerful free kick.
Catania almost responded immediately through Keko, who smashed a strike from the edge of the area against the bar.
The visitors 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.
Napoli 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.