The German international scored from the edge of the box with childlike ease after Aaron Ramsey's superb run and setup. Giroud added the second after an incredible piece of skill by Ozil left the Frenchman with the goal at his mercy.
At the beginning of this campaign, Group F was easily the hardest on paper. The Gunners, however, have eased to two wins and now stand on the precipice of qualification for the knockout stages.
The win over Napoli was comfortable but came thanks to a number of outstanding performances from the men in red and white.
Ramsey was superb, once again, and dominated and dictated the tempo from midfield as Jack Wilshere looked on from the dugout. Ozil was simply sublime and his clever movement and vision had Napoli tied in knots all evening.
The returning Mikel Arteta gave a great reminder that he still has a huge amount to offer, as did Tomas Rosicky. The backline were solid and never looked like being penetrated, and Giroud continued his fine form in front of goal.
In short, it was one of the great Champions League nights for Arsenal and their legions of fans.
Here, Bleacher Report offers six things we learned from Arsenal vs. Napoli...
Arsenal's first-half performance was one to savour.
It gave a reminder to Europe of just how good the Gunners can be when they put their minds to the task at hand.
Before the game, Arsene Wenger said he felt his team were Champions League contenders this year. Many pundits and analysts would have scoffed at the veteran's boast. However, after this performance against Napoli, their thinking might be revised.
Speaking to Sky Sports, Wenger said;
You always think 'let's do it' every year, and one year it will go for you, so let's hope it will be this year.
If we get out of the group I would say we have a chance [to win the Champions League], but what we have to show is that we have the strength.
It is something I miss [the Champions League trophy] that I will try to fight very hard to fill my CV with.
After making a quality side like Napoli look less than ordinary, the Gunners might actually be a good outside bet for the trophy with big ears.
Napoli were a beaten side before they even took to the pitch against Arsenal.
As soon as Gonzalo Higuain pulled out with an injury, per the Daily Mail, the Naples-based side were on a hiding to nothing.
Higuain has been excellent for the Serie A side so far this season. The ex-Real Madrid centre-forward gives his team a superb out ball and provides great penetration for his teammates.
Two of the most important, misunderstood and underestimated aspects of centre-forward play are penetration and mobility.
The centre-forward provides his team with positional play that will allow penetration of the opposition and it is mobility that gets him there.
The Argentinean international provides both to great aplomb. These are the main reasons that Arsenal were linked with Higuain during the summer.
Goran Pandev, more used to a deeper creative role, was thrown in as striker by Rafael Benitez. He rarely kept the striker's position and this allowed the Arsenal back four to squeeze up towards midfield. This then gave their highly-mobile midfield the chance to overload Napoli's midfield men and from there the match was lost.
For a great example of what Napoli missed all one had to do was watch Olivier Giroud. The ex-Montpellier man was outstanding all night. He provided penetration for his raiding midfielders and brought the wider men, Mesut Ozil and Tomas Rosicky, into the game.
in short, Ozil may have taken most of the plaudits from the game but Giroud was easily Arsenal's most important player.
As soon as Ozil's first goal for the club hit the back of the net, there was no way back, but the game was over as soon as the ex-Arsenal target picked up a calf strain.
Arsene Wenger has signed some fabulous players in his time at Arsenal.
The list is endless.
Patrick Vieira, Emmanuel Petit, Thierry Henry, Aaron Ramsey, Jens Lehmann and Sol Campbell are just a few of the great, great players who have thrilled crowds at Arsenal since 1996.
In just five games, Mesut Ozil has staked the biggest claim possible for a place as a future Arsenal legend.
He has the ability to lead this team to heights undreamed of in the last couple of seasons.
If he keeps up his current form, he will be in the running for Premier League player of the season. But to win that prestigious award, he might have to get past Aaron Ramsey.
David Moyes would have been far better served signing Mesut Ozil instead.
Since joining Arsenal, the German international has been sensational. He has waded in with five assists and one goal in just five games for the club.
In short, Ozil has lived up to the hype.
The 24-year-old with the silky skills has slotted into the Gunners' midfield as if he has been playing there all his life.
His intelligent movement, vision, passing ability and skill are so good that he stands above almost every teammate in one of the most technical teams in the world.
Ozil is so good it would take a miracle for him not be a success, which makes you wonder why United, a team bereft of creativity in centre midfield, never even entered the running for the star.
In early September I wrote this piece stating that United should have gone for Ozil instead of Fellaini.
A number of days later, Teddy Sheringham, a Champions League winner with United in 1999, told Ian Wright on his radio show, per the Daily Mail, that United should have gone for Ozil.
Looking at the Arsenal's and United's progress this season, it is hard to see why they did not.
United's loss is Arsenal's gain in every which way, shape and form.
Have the Gunners ever put in a more complete performance in the Champions League?
There have been many memorable Champions League nights for Arsenal but rarely have they played so well.
Admittedly Napoli, wearing the worst-ever jersey, as per the Dirty Tackle, put in a poor performance. They badly missed Gonzalo Higuain, but that belies just how good Arsenal were in the first 45 minutes.
Napoli were only missing one key player and they were thoroughly outplayed in every section of the pitch. Arsenal just swept them aside.
They dominated midfield and defence and Olivier Giroud scored his third goal in his last five Champions League games.
If the first half was a tale of Arsenal dominance, the second was a tale of their discipline and professionalism. Napoli had nothing to lose and tried to get back into the game, but Arsenal squeezed the game and gave the Serie A side practically no chances.
This aspect of Arsenal's play was probably the most impressive.
In the past, Arsene Wenger's team would have kept going at 2-0 and tried to score three, four or even five. In doing this, they would have undoubtedly conceded at least one goal.
This time around the Gunners played like the Italian team and shut their opponents out of the game by containing their midfield.
There is little doubt that Arsenal will play far better sides than the Napoli one they played tonight, but every sign from this match was positive.
Arsenal, after beating Marseille in Matchday 1 and hammering Napoli in Matchday 2, are on the verge of qualifying for the round of 16.
The way the Champions League fixture list has been put together this season means that the Gunners have the advantage of two games at home in a row before the end of October.
Arsene Wenger's team travelled to Marseille for the first game of the mini campaign and came away with a deserved win. They then outplayed Napoli in the second game to sit atop Group F with six points.
Their next game is at home to Borussia Dortmund on October 22.
If the Gunners win on October 22, they will have nine points. Napoli, who take on pointless Marseille, would need to win to have six points while Dortmund would have just three after losing to Arsenal.
Napoli and Dortmund would have to face each other again, which means that Arsenal are virtually guaranteed a place in the knockout stage if they beat Dortmund.
Having won the last 10 games in a row, in all competitions, who would bet against Arsenal collapsing and not qualifying?
Statistics courtesy of UEFA.com, WhoScored.com, Arsenal.com, PremierLeague.com