The ex-Real Madrid playmaker then turned provider seven minutes later when he took advantage of some lax defending to race to the right-hand byline and cut it back for Giroud to double the lead.
It was no more than the home side deserved as they marked the 17th anniversary of Arsene Wenger's Arsenal arrival with a mesmeric first half showing that condemned the Italians to their first loss under Rafael Benitez.
Napoli rarely threatened and clearly missed the influence of Gonzalo Higuain who was ruled out through injury. The Argentine had dominated the pre-match chatter after appearing to snub a move to the Emirates in the summer but he cut a forlorn figure as he watched from the stands.
The result means Arsenal sit top of Group F, three points clear of both Napoli and Borussia Dortmund.
PRE-MATCH - Higuain OUT, Wilshere on the bench - Napoli pipped Arsenal to the signing of Higuain in the summer and all eyes were on the team sheet to see if the Argentine would feature. In the end it was an anti-climax as the ex-Real Madrid man was deemed unfit to make the bench. Meanwhile, Arsene Wenger sprung his own surprise by giving midfielder Jack Wilshere a rest and a place amongst the substitutes.
8’ GOAL: Arsenal 1-0 Napoli - Fabulous opener. Ramsey rampages down the right and fizzes a low cross into the path of Ozil who steers a stunning left-footer into the corner from 18 yards out. A sublime goal and a great way to break your Gunners duck.
15' GOAL: Arsenal 2-0 Napoli - A belated birthday gift for Giroud as Ozil takes advantage of a Napoli mix-up to race to the right-hand byline and cut the ball back for the Frenchman to do the rest.
48' CHANCE - Half chance for the hosts. Another Arsenal attack sees them slice through the Napoli rearguard down the right through Giroud. The French ace surges to the byline and cuts it back for Rosicky who misses his kick at the near post.
76' GREAT SAVE - Reina somehow keeps out Koscielny's volley after Arteta had flicked on a right-wing cross.
90' CLOSE - Wilshere drives to the left byline and fizzes a low cross into the area that Giroud is millimetres away from converting.
Arsenal have kept a clean sheet in each of their last six home games against Italian sides, qualifiers included (5 wins, 1 draw).
The defeat was Rafael Benitez's first as Napoli manager.
The win was the perfect way for Arsene Wenger to mark 17 years to the day that he first arrived at Arsenal.
Benitez has never managed a winning side away at Arsenal losing six and drawing four of his visits as a coach.
That was Wenger's first ever win over Benitez in the Champions League at the fifth attempt.
Napoli have still not won a competitive match in England.
TALKING POINT - Can Arsenal win the Champions League? Arsene Wenger spoke about his belief they can do it this season prior to kick off and the way his team blew away Napoli in the opening 15 minutes would have sent shockwaves around the rest of Europe. They have some real talent in possession of the ball. The question is whether they have the character and defensive discipline - as well as the strength in depth - to go all the way.
MAN OF THE MATCH - Mesut Ozil (Arsenal): At the heart of all of Arsenal's attacking play in a barnstorming first period. Netted his first for the club and teed up the second for Giroud.
PLAYER RATINGS -
ARSENAL: Szczesny 6, Sagna 6, Gibbs 6, Mertesacker 6, Koscielny 6, Rosicky 6, Arteta 7, Ozil 9, Ramsey 8, Flamini 8, Giroud 8. Subs: Wilshere 7, Monreal 5.
NAPOLI: Reina 7, Mesto 6, Albiol 5, Britos 5, Zuniga 6, Inler 6, Behrami 6, Callejon 6, Hamsik 6, Insigne 6, Pandev 5. Subs: Mertens 5, Zapata 5, Fernandez 5.
THE MATCH IN A TWEET