The hosts were on the backfoot right from the start as Pablo Alvarez was sent off in the second minute.
Walter Mazzarri's side created their first chance in the 17th minute when Goran Pandev took an attempt on the home team's goal from outside the box.
However, Pandev failed to keep his attempt on target.
Blerim Dzemaili met with the same fate when he tried his luck six minutes later before Mariano Andujar saved Pandev's effort.
The Naples outfit continued to dominate proceedings and test the Catania defence, with Edinson Cavani coming close twice in the final minutes of the first half.
The Azzurri went close a number of times to breaking the deadlock in the second 45 minutes, with Pandev, Cavani, Lorenzo Insigne, Marek Hamsik and Eduardo Vargas all trying their luck but in vain.
Napoli were almost denied a point at Stadio Angelo Massimino in the final stages of the contest, when Alejandro Gomez rattled the post with a right-footed shot from the left side of the area.