Some players can spot a pass that slices a defence open and some players are capable of putting the ball roughly where their team-mates want it, but few can do it with the same level of precision as Özil.
In the space of half an hour, Arsenal's record signing had created three goalscoring opportunities. These were not just passes played into the feet of a team-mate or into space, they were played exactly where they needed to be gathered at full speed or hit first time.
Özil deals in millimetres, like a snooker player making sure he not only pots the red, but leaves himself ideally placed to rattle in the black. Bigger tests await him and teams will try to find a way to limit the time and space he has, but Özil created more goals than any other in European football over the last five years.
Özil pulled the strings as though he had been Arsenal's puppet master for years and it took him just 11 minutes to secure his first assist. Taking down Kieran Gibbs's long ball, he delivered a perfect low cross for Giroud to sweep in first time.
Had it not been for Sunderland goalkeeper Keiren Westwood Arsenal would have gone in at half-time with a huge lead, although he was helped by some poor finishing from Theo Walcott.
Walcott has the pace to get in behind defences and Özil has the vision to find him. Unfortunately for the England man, he could not show the same clinical execution.
Twice Walcott was left with only the goalkeeper to beat, twice he shot too close to Westwood. He also missed badly with a header when picked out by Jack Wilshere and shot straight at Westwood from a Giroud flick.
Sunderland had been outclassed, but all their centre-back Modibo Diakité seemed interested in was asking Özil for his shirt. Given the runaround they had been made to suffer, maybe he wanted to see what it looked like close up.
Souvenir hunting will not impress manager Paolo di Canio, although little would have in a dire first period for the home side.
Sunderland hit the crossbar with a Diakité header and Jozy Altidore's swerving shot was parried by Wojciech Szczesny, but the Gunners dictated play.
That changed at the start of the second half when Laurent Koscielny gave away a penalty for a foul on Adam Johnson. Replays suggested Johnson had fallen over his own feet, but it was a needless tackle and substitute Craig Gardner tucked away the penalty.
Sunderland briefly made Arsenal worry, but the visitors took the lead again when Aaron Ramsey volleyed home Carl Jenkinson's cross.
Then came the game's most controversial moment. Altidore won a tussle on the edge of the area with Bacary Sagna and his shot trickled over the line.
Sunderland thought they had equalised, Arsenal thought referee Martin Atkinson had blown for a foul on Sagna. He had done neither, instead pulling play back to book Sagna, much to the dismay of the Black Cats.
Arsenal wrapped up the three points minutes later when Özil and Giroud combined to set up Ramsey for his second.
"We should have scored more in the first half," added Wenger.
"Theo Walcott could not finish today, but even though Sunderland put us under pressure, we came through it and found two goals after they had equalised at a good time for them."
Di Canio's emotion got the better of him in stoppage time and Atkinson sent the Italian to the stands to contemplate a defeat that leaves the Black Cats bottom of the table.
"Arsenal dominated the first half, but we played with determination, desire and quality in the second," said Di Canio.
"If we play like that we will have a good season.
"I said to the referee 'if you want to have a perfect day you should send me off.' He did, but I'm sure he's a good person."
Sunderland (4-4-2): Westwood 6 Celustka 6 Diakite 6 Roberge5 Colback 5 Johnson 6 Ki 5 Vaughan 4(Gardner ht) Mavrias 5(Borini 71)Altidore 7 Fletcher 5 (Wickham 77).
Subs not used: Mannone, Brown, Larsson, Cuellar.
Arsenal (4-2-3-1): Szczesny 6 Jenkinson 7 Sagna 6 Koscielny 5 Gibbs 7 Ramsey 8 Flamini 7 Walcott 6 (Monreal 85) Özil 8 (Vermaelen 80) Wilshere 7 Giroud 8.
Subs not used: Fabianski, Frimpong, Miyaichi, Akpon, Gnabry.
Booked: Sagna, Flamini.
Referee: M Atkinson (W Yorks).