In a pulsating start, he German caressed home an Aaron Ramsey cross on eight minutes, having been found unmarked by the Welshman on the edge of the penalty area.
Ozil then capitalized on some slack Napoli defending from its own throw-in by surging to the byline and squaring for Olivier Giroud to double the Gunners' lead, and the advantage proved decisive.
Arsene Wenger – celebrating 17 years in charge of Arsenal - welcomed back Rosicky from a thigh injury to replace Serge Gnabry, while Mikel Arteta came in as Jack Wilshere was rested.
Gonzalo Higuain - who was a transfer-window target for Wenger's side - was unable to shake off a calf injury in time to feature for Napoli.
Arsenal was at its free-flowing best right from the off and was soon two goals ahead.
The first came in just the eighth minute when Ramsey stormed down the right-hand side and cut back for Ozil on the edge of the box and the German hit a sublime first-time shot that nestled in the corner.
And the home fans celebrated a second after quarter of an hour. Giroud flicked to Ozil in the box and he stormed to the byline before laying back for the Frenchman to tap home from close range.
Napoli almost responded when Miguel Britos made a late run into the box from a Lorenzo Insigne corner and headed wide when unmarked.
Arsenal continued to dominate with Ozil and Ramsey producing a midfield masterclass. The latter twice saw shots blocked in the area by Raul Albiol.
The home side's lead was almost extended immediately after the restart when Giroud raced clear on the right and fed into the path of Rosicky six yards from goal, but he failed to make good contact when under pressure from Britos.
Napoli tried to come back into the contest and Insigne twice saw efforts go just wide, while Gokhan Inler blazed harmlessly over with 20 minutes remaining.
Laurent Koscielny then had a wonderful opportunity to add a third when he met Arteta's flick but from point-blank range he fired straight at Pepe Reina.
But Koscielny's miss made no difference to the final score as Arsenal moved to the top of the group. The club's next Champions League fixture is at home to Borussia Dortmund on Oct. 22.