Ramsey netted the first after just five minutes when he reacted swiftly to Asmir Begovic's save from Ozil's free kick. The Welshman prodded home his eighth goal in 10 games and his fourth in the last three.
From there the Gunners looked very comfortable as they stroked the ball around with ease. To their credit, the ever-improving Potters ground their way back into the game and deservedly equalized after Geoff Cameron slotted past Wojciech Szczesny from fully 18 yards.
Perhaps against type, the Gunners then took the lead from a corner as Mertesacker climbed highest to reach a dangerous Ozil corner to flick the ball into the back of the net. The irony of Arsenal scoring a Stoke-style goal was not lost on their fans as they roared with approval.
Sagna's late goal, from Ozil's third assist of the day, finished the game as a contest, but it came against the run of play with Mark Hughes' team well on top.
The Gunners may have won 3-1, but this was far from a comfortable victory.
Here, Bleacher Report offers six things we learned from Arsenal vs. Stoke City.
Mesut Ozil finally made his home debut after enjoying something of a dream debut against Sunderland last weekend.
The German international created the opening goal for Olivier Giroud against the Black Cats and his on- and off-the-ball intelligence shone through. The same cannot be said of his Champions League debut for the Gunners against Marseille.
Ozil was largely anonymous in a disappointing game for the neutral. The adrenaline rush of making his debut got him through his first game but could not sustain him through the match in France.
Arsene Wenger, surprisingly, decided to heap pressure on the 24-year-old right from the start of his Arsenal career by comparing him to Gunners legend Dennis Bergkamp. Le Prof, per Jason Burt of The Telegraph, said:
Yes, he is a similar type (to Bergkamp).
Dennis was maybe more prolific. Dennis was first a striker but he created as well. But Dennis’s evolution through his career was an adaptation to his physical qualities. When he couldn’t score any more he became a great provider.
I think Ozil, at the start, has more a midfielder's mentality and Dennis, at the start, had more a striker’s mentality. But he [Ozil] can score, yes.
He will need time to adapt to Arsenal's and the Premier League's style, but on current viewing that should not take long.
Against Stoke City, Ozil was everywhere until he ran out of steam.
At times he popped up in the right-back position, and at others he could be found anywhere across the attacking midfield three. He even rotated with Ramsey and Mathieu Flamini in center midfield.
It's still a bit of a stretch to say he is the next Johan Cruyff, but he does have the ability to become the Premier League embodiment of Total Football.
Prior to this game at the Emirates Stadium, Stoke City had not won in 10 visits to Arsenal, so the odds of Mark Hughes inspiring a win were slim at best.
Under Tony Pulis, the man Hughes succeeded, the Potters were always a belligerent side. They were tough to break down and offered little on the creative and attractive side of the game. They were, however, a perfect example of how to run a smaller club in the Premier League on a limited budget.
Hughes has come in, and in just five games he has begun to change the style of football at the club. Stoke will always remain loyal to their financial philosophy, but they are eager to appeal to more fans. This is the main reason for change at the Britannia.
The system has been tweaked from a 4-4-2 to a variation of a 4-5-1. While they are still struggling somewhat to create chances, their style of play has changed almost completely. They are no longer a long-ball team and mix their style up far more than in previous years. Against Arsenal, their patience caused many problems for the Gunners' re-adjusting backline.
At the beginning of the season, they were fifth favorites for relegation on Oddschecker. Today they are ninth-favorite, and that is testament to Hughes despite the loss.
Jack Wilshere has received a fair amount of flak from unhappy fans this season. While Aaron Ramsey's form and Mesut Ozil's inspired signing have captured the imagination, Wilshere has been criticized by some for not being back to his best. He is, however, the key player in Arsene Wenger's team.
In the build-up to the Stoke City match, Wenger moved to remind fans that the England international is still on the road back from injury.
Talking to Sky Sports News, Wenger addressed the unfair comparison to Ramsey:
There are similarities (to Ramsey) because it takes time to come back to your best physically.
However, you could consider Jack was ahead of his age before he was injured, it is not the same. Aaron Ramsey had to make his way there.
For Jack, I think it is more a fitness problem than anything else, but that will come back much quicker than the rest.
Aaron had heavy metal in there (to pin his double leg break), and also the psychological impact of the injury, it took him a while to get back. When he was injured he was not there, he was still in a development phase.
Fitness wise Jack is between 80-90 percent of his potential. For the rest, he has not a lot to learn - he understands the game, can play anywhere, defensive midfield, central midfield. He is a complete player.
What Arsenal fans need to realize is that Wilshere is sacrificing his game for the greater good. There is little doubt that Wilshere will eventually partner Ramsey in center midfield and usurp Flamini. For the moment, however, he is being played out of position to accommodate Flamini and Ozil.
When he returns to 100 percent fitness and his natural position, the Gunners will go from strength to strength.
Mark Hughes could have pulled off a real transfer coup with the capture of Marko Arnautovic.
The colorful 24-year-old has always shown potential, but he has been deemed something of a high-risk venture. He made his debut for FC Twente in 2006 after impressing in the Dutch team's underage squads. From there he was snapped up by Inter Milan on a season-long loan deal in 2009.
Jose Mourinho, however, decided not to sign the youngster on a permanent deal after criticizing him publicly. Arnautovic then signed for Werder Bremen. In July, Stoke City paid Werder Bremen £2 million for his signature, according to the BBC.
The youngster made his first start of the season against Arsenal. While he did not set the world on fire, he showed enough potential to suggest that Stoke may have got a bargain.
He worked hard up and down the left flank against Arsenal's debutant Serge Gnabry and played a pivotal role in Stoke's equalizing goal. During the goal he showed clever movement and a laconic technique that reminds of Dimitar Berbatov at his best.
Confidence is a beautiful thing.
Aaron Ramsey just can't stop scoring. The Welshman has been the Premier League's best player in the opening month. He has scored eight goals in 10 games in all competitions.
Scoring against Stoke City will always be an enjoyable experience for Ramsey. It was in 2010, against the Potters, that the youngster's career was almost ended by a reckless Ryan Shawcross tackle.
Since then, and some 80 games later, Ramsey is finally returning to the potential he had shown when he first broke into the Arsenal team. His high mobility, tenacity, composure and confidence have brought his game to the next level.
He still has much to learn, though. In the second half Steven N'Zonzi and Marc Wilson dictated the tempo of the match, and Ramsey and Flamini struggled to gain a foothold. Tough games like this are the making of any player. More can be learned from adversity than from easy games.
Stoke City's equalizer came from a simple and beautifully flighted pass by Steven N'Zonzi to Marko Arnautovic.
The Austrian international had drifted from his position on the left into the center-forward position. He completely evaded both Bacary Sagna and Per Mertesacker in doing so. His effort cannoned off the post before it was put away by Geoff Cameron from the edge of the box.
Minutes later, Robert Huth replicated N'Zonzi's pass, as this time Laurent Koscielny and Kieran Gibbs became mixed up to gift the visitors another chance.
Giving up these type of chances is criminal at the highest level. They are, however, easy to eradicate. Arsenal will need to iron these flaws out of their system if they are to have a say in the Premier League title.