The Welsh and German international's were simply brilliant as Arsene Wenger's slick passing side deservedly won the match. They did, however, have much to thank Martin Atkinson for as the Yorkshire-based referee made a number of strange decisions.
Sunderland were outplayed to an incredible extent in a first half where Ozil did not put a foot wrong and where Arsenal really should have scored at least four or five goals. The Black Cats responded well in the second half and equalized early. Ramsey then grabbed the match by the scruff of the neck and scored two stupendous goals to win the game for the Gunners.
Paolo Di Canio was then sent off at the end of the match after he challenged the referee on his strange decision.
Here, Bleacher Report offers six things we learned from Sunderland vs. Arsenal...
Mesut Ozil, Arsenal's record signing, had a debut to remember.
In many ways this game against a limited Sunderland side was the perfect introduction to the Premier League for the German international.
With superior movement and simply incredible technique and vision, Ozil stood out among one of the most technically proficient teams in Europe. His eye for a pass is phenomenal, and there can be little doubt that he will bring a new level of goals, assists and danger to Arsene Wenger's team.
As opening games go, Ozil was excellent and gave plenty of reasons to expect more in the future.
Arsenal at the Stadium of Light was always going to be a frightening prospect for Paolo Di Canio and Sunderland.
The Gunners have made an art form of beating limited teams in the past. With the Black Cats well short of class this was always going to be a upward battle.
Why Di Canio decided to send out his team in a 4-4-2 against Arsenal's fluid 4-2-3-1 is anyone's guess. Di Canio, surprisingly, sold Stephane Sessegnon to West Bromwich Albion during the summer transfer window.
Without the Beninese international they lack creativity in any form. They most importantly, however, have rid themselves of their best advanced center midfielder.
Arsenal overload teams in midfield with a fluid triumvirate, of which Ozil in now a major part, and quite simply, they gave the Black Cats the runaround.
Di Canio then brought on Craig Gardner and strengthened midfield for the second half. Gardner scored a penalty within minutes of coming on.
In the end the Italian's team were outdone by some suspect refereeing and by Arsenal's slick game, but they were better in the second 45.
They are far from safe from relegation and will need to get their tactics right from the start of every game if they are to avoid the dreaded drop.
Patrons of NBA Jam will be familiar with the phrase "He's on fire!" Giroud is that man in football terms.
The Frenchman did not enjoy a stellar debut season with the Gunners. He even found himself left out of the team on occasion as Wenger thought he was coping poorly with the pressure of playing for a top club.
He lacks pace, an international-quality first touch and possesses no real creative vision. His lack of vision can be seen in only one key pass per game and just 0.3 dribbles per game last term.
He does, however, possess a fearsome physical presence and is developing a great understanding with one of the most creative midfield's in world football.
So far this term, the big Frenchman has scored four goals in four games and is on fire. He has also begun to add assists to his game and played a key role in Aaron Ramsey's second goal.
Giroud received a heavy knock towards the end of the game and was eventually replaced by Chuba Akpom. His form and importance will guarantee than each and every Arsenal fan will monitor his injury status closely as the Champions League group stage approaches.
Sunderland fans have every reason to feel hard done by after Martin Atkinson's bizarre handling of Bacary Sagna's foul on American international Jozy Altidore.
Altidore was played into the box by Craig Gardner's slide rule pass. Sagna, however, was caught slightly out of position and was too close to the forward to react to the pass. His solution was to grab the giant American around the shoulders and hold him back.
To his credit Altidore shrugged the Frenchman off with an incredible show of strength and passed the ball past Wojciech Szczesny for a goal.
Somehow the referee called the play back to outside the box and awarded a free-kick to Sunderland. He, in effect, disallowed the goal and refused advantage to Sunderland. On top of that he only gave Sagna a yellow card for an obvious professional foul.
In short, Sunderland were robbed.
Di Canio, incensed by the decision the berated the referee at the end of the game and, to rub salt into festering wounds, was sent off.
A bad day all around for Di Canio and Atkinson.
At the beginning of the season I wrote an article stating that Aaron Ramsey was on the verge of becoming Arsenal's most important player.
His two goals and all around performance against Sunderland have done nothing to detract from that distinctive possibility.
Ramsey was brilliant in midfield today and is growing with each and every game. He is still suspect defensively though. He has to be the most disciplined member of Wenger's team as Jack Wilshere, Mesut Ozil, Tomas Rosicky, Theo Walcott and Santi Cazorla all do their best work in the final third.
He has one thing that none of the others possess; a phenomenal set of lungs.
Ramsey has the stamina and ability to cover every blade of grass on the pitch and the way he took his two goals, particularly the first, speaks volumes of how he is getting more and more confident with each touch of the ball.
As good as Ozil is, and he is incredibly good, the signing of the German international will not paper over Arsenal's shortcomings.
The Gunners have a minor problem in center midfield in that many of their players are very similar. They are lightweight and lack physicality and defensive nous. Johnathan Wilson, in his column for Bleacher Report, pointed these frailties out most recently.
Arsenal lack players with core defensive skill sets in midfield and as such that deficiency often exposes their slow center-defenders. This happened when Adam Johnson was allowed to run at Laurent Koscielny and be fouled by the Frenchman for Sunderland's equalizing penalty.
Ozil has brought class, skill and thrills galore to their attack, but his capture hasn't fixed their physical and defensive frailties.
In many ways the Gunners may have been better suited with a player like Marouane Fellaini instead of Ozil at this stage of their development.