The German playmaker netted his first goal for the Gunners just eight minutes into what looked like being a tricky continental hurdle for Arsene Wenger's side to overcome, but ended up being one cleared with consummate ease.
Ozil was picked out on the edge of the box by Aaron Ramsey and crashed a stunning half-volley into the back of the net past a helpless Pepe Reina.
He was to have Napoli on the ropes again seven minutes later, with a neat cut back turned home from close range by Olivier Giroud - another of those whose star continues to shine brightly at the start of the 2013/14 campaign.
It was a 10th straight win in all competitions for Arsenal, who have stormed to the top of the Premier League and now look on course for safe passage through to the knockout stages of Europe's elite club competition.
The Gunners swept into the lead on eight minutes with a goal of the highest quality.
Giroud, who turned 27 on Tuesday, laid the ball out to the right as Ramsey darted clear. The Wales midfielder, enjoying a fine personal start to the new campaign, strode towards the by-line before looking up and clipping a perfectly weighted pass back towards the penalty spot. Ozil arrived on cue to cushion an instinctive half-volley past former Liverpool keeper Reina to open his Arsenal account in some style.
Before Napoli - missing injured Argentina striker Gonzalo Higuain, who was one of Wenger's summer targets - could mount a recovery, they trailed 2-0 on 15 minutes.
Giroud latched on to a poor throw-in to find Ozil on the right. The German playmaker, signed from Real Madrid, waltzed past his markers and into the penalty area before cutting a pass back to Giroud, who had continued his run on through to the six-yard box and the France forward promptly crashed home his sixth goal from close range.
Rafa Benitez had talked about the need to calm the euphoria following Napoli's home win over last season's beaten finalists Borussia Dortmund on matchday one.
But for the former Liverpool boss, who guided Chelsea to Europa League success while interim manager last season, it was very much a case of damage limitation before his side had even got a chance to take the match to the Gunners.
Napoli had tried to raise their game before the break and defender Miguel Britos sent a towering header over the Arsenal crossbar following a corner.
However, any thoughts of a recovery were short-lived as Arsenal were soon back on the offensive - with Ramsey and Ozil the main agitators of the Italian's overworked rearguard.
With just under half an hour to go, Wenger replaced Tomas Rosicky with Jack Wilshere, but the tempo of the match had already long dropped by then.
It should have been 3-0 on 75 minutes when Mikel Arteta's flick-on through a crowded box was met by Laurent Koscielny, but his snapshot was straight at Reina from point-blank range.
With Dortmund beating Marseille, Group F is now very much Arsenal's for the taking, with a double-header next up against the Germans.
On this evidence, Wenger's men may well be ready to make a serious tilt at going one better than Jurgen Klopp's side in 2014.