Jack Wilshere teed up the win with his opener, but another man of the moment, Aaron Ramsey, made sure that his midfield colleagues did not steal all the headlines as he carried on his red-hot form with another goal.
Transformed from the opening day of the season, when they lost 3-1 at home to Aston Villa, the Gunners have remained unbeaten since.
Wilshere scored his second goal in as many games when he struck in the first half and Ozil got on the goal trail with a second-half header.
At times Norwich had rare skirmishes in the Arsenal half and went close through Robert Snodgrass and Lee Martin.
Jonny Howson eventually found a way past home goalkeeper Wojciech Szczesny to grab a consolation and set up a tense final 20 minutes, but Ramsey and Ozil had the final say.
The early groundwork for the victory had to be done without Ramsey, Arsenal’s player of the month for the third time in a row, as he was rested.
Spanish playmaker Santi Cazorla was drafted in alongside Wilshere and German star Ozil in an attacking trio full of flair and creativity.
With a team crammed full of international midfielders, there was little wonder that Arsene Wenger’s side spent the majority of their time camped in Norwich’s half.
Still, visiting goalkeeper John Ruddy was not tested as much as Wenger would have liked, as his side initially did a lot of work in midfield without any end product.
Right-back Bacary Sagna was allowed space and time to get down the flank past Martin Olsson, only to either overhit a cross or watch it cleared away.
A change of approach was needed, and as soon as the Gunners went through the middle, they broke the deadlock.
Cazorla carried the ball forward before picking out Wilshere in space just on the edge of the 18-yard box.
In turn the England ace played a neat one-two with striker Olivier Giroud before coolly tucking the ball past Ruddy from the Frenchman’s flick.
With Norwich struggling to get a foothold in the game, the only disappointment for Arsenal was the sight of midfielder Mathieu Flamini departing after a 30th-minute clash of heads with Alexander Tettey. Ramsey took his place.
As Arsenal pushed for a second, Ruddy showed his England credentials when he made a reaction save at his near post as Giroud attempted to turn home Kieran Gibbs’s cross from the left.
Russell Martin fired wide of Arsenal’s goal soon after the interval in a warning shot for the hosts.
However, within 10 minutes, the Gunners had doubled their lead as Giroud’s cross was met by Ozil and he buried a header past Ruddy to calm the nerves of the home fans.
They were on the edge of their seats again in the 70th minute, however, when Howson drilled home from just inside the box after Per Mertesacker failed to clear an Elliott Bennett cross.
It fell to the in-form Ramsey to put the game to bed with seven minutes to go, jinking into the box and slamming home his 11th goal of what is turning into a remarkable season.
Ozil added his second of the day in the 88th minute as Arsenal fired another warning shot to the rest of the league.