The Gunners were evenly matched with the defending champions when the match kicked off, as City were without both Toure brothers, Sergio Aguero and Samir Nasri, while Mario Balotelli was relegated to the bench.
But that changed when Laurent Koscielny was sent off after nine minutes.
The Frenchman, whose inclusion in the starting XI over Per Mertesacker raised a few questions, tackled Edin Dzeko in the box, and was deservedly shown a red card. Wojciech Szczesny did very well to save Dzeko resulting penalty, but the game was already lost.
There was really no way for Arsenal to defeat the defending champions with 10 men, and James Milner sent that message loud and clear in the 21st minute.
Slipped through by Carlos Tevez and given space by Thomas Vermaelen, Milner smashed his first-time shot just inside the far post, and there was nothing Szczesny could do about it. 1-0.
As City grew in stature and looked to seal the game early, Edin Dzeko atoned for his penalty miss with a tidy tap-in right after the half-hour mark.
Milner's ball across goal was met by Carlos Tevez and saved by Szczesny, but the Bosnian was perfectly placed to knock the loose ball home and make it 2-0.
It was apparent after the first half that there was no way back for Arsenal. The Gunners put in a commendable second half performance, but even with Vincent Kompany's red card, the gap was too large to bridge.
Let's take a look at each Arsenal player's performance. As always, if you disagree with my ratings, let me know in the comments or on Twitter.
Per Mertesacker: 7.5
As always, Mertesacker put in a consistently above-average display. Arsene Wenger will only wish he started him instead of Laurent Koscielny.
Good in the air, strong in the challenge and intimidating going forward, he dealt with Edin Dzeko's powerful aerial threat well. Certainly better than Koscielny did, anyway.
Olivier Giroud: 7.5
According to Arsenal stats man 7amkickoff, Oliver Giroud had more touches after coming on in the 57th minute than Theo Walcott did all game. That underscores Giroud's work ethic as much as it does Walcott's malaise.
He was the ideal target man for an Arsenal side that often resorted to good old kick-and-run football, getting on the ends of a couple free-kicks and crosses and providing as much of a goalscoring threat as anyone else on the pitch for the Gunners.
Aaron Ramsey: 8
The much-maligned Welshman replaced Abou Diaby just after the hour mark and showed why he should have started in the Frenchman's place.
He constantly tried to move Arsenal forward with driving runs and forward passes, slipping a delicious through-ball to Theo Walcott late in the game that would have found the back of the net if it wasn't for a heroic Joleon Lescott clearance off the line.
Look for Ramsey to get more playing time in his natural central midfield position in the near future.
Wojciech Szczesny: 8
Szczesny was helpless on both goals, and at the mercy of his threadbare outfield for most of the game.
When he did get involved, though, he produced a couple moments of magic. Szczesny athletically saved Edin Dzeko's penalty to give Arsenal a glimmer of hope after the red card, knocking the ball off the post with his foot and holding the rebound.
And when Carlos Tevez raced through one-on-one in the second half, he intelligently stood his ground and did just enough to poke the ball off the striker's feet as he wound up to shoot. Top-class goalkeeping.
Bacary Sagna: 6.5
Sagna improved upon his recent substandard displays with an impressive one against Manchester City.
He was forced to work a bit harder than usual due to the absence of a winger in front of him (Alex Oxlade-Chamberlain was hauled off after Koscielny's red card), but still managed to get forward productively and make a series of defensive headers and clearances.
Laurent Koscielny: 2
Normally, I'd say that a player who only lasted nine minutes does not merit a rating, but unlike most players who are on the pitch for such a short time, Koscielny made a meaningful contribution to the game.
He all but lost the game for Arsenal when he tackled Edin Dzeko in the box rather unnecessarily, with technique that many American football coaches would be proud of.
A three-match ban in the middle of Arsenal's most hectic period of the season is not what the Gunners need.
Thomas Vermaelen: 6
I really struggled with Vermaelen's rating because he was such an equally important part of Arsenal's pugnacious second half and Manchester City's two goals.
The captain was almost completely at fault for City's first, allowing James Milner the space to capitalize on Carlos Tevez's through-ball and fire a laser inside the far post.
And on their second, Vermaelen didn't close down Milner fast enough to prevent the ball across goal that eventually found Edin Dzeko.
Yet he was strong in the challenge and out of breath by the end of the match from the running he was doing all over the pitch. He was Arsenal's defensive lion in the second half, and therefore gets a slightly above-average rating.
Kieran Gibbs: 6.5
Perhaps the fact that both of Manchester City's goals came from the left side of Arsenal's defense says something about Kieran Gibbs' performance, but there were more positives than negatives.
When Arsenal got forward, especially in the second half without the aid of Lukas Podolski, Gibbs was an outlet on the left. He worked as hard as he always does in both attack and defense, making some decent stops and delivering a couple good crosses.
Abou Diaby: 5.5
Credit to Diaby for working his way back from injury yet again, but he should not have started this game.
The Frenchman looked well off the pace and very rusty with his first touches and passing, which should be expected of a man who has not played a senior match since September.
The biggest positive is that he made it through an hour without injuring himself, but he should not start Arsenal's next game.
Jack Wilshere: 10
Wilshere delivered an absolute virtuoso performance in midfield. When those around him looked to be tiring and falling back to stop City's onslaught, he grabbed his team by the neck and drove them forward.
He constantly got dirty, fighting for the ball and throwing himself into tackles in all areas of the pitch. Wilshere even leapt to clear a Javi Garcia header off the line. Whether or not Vincent Kompany's red card was justified, the fact that Wilshere ran into it is indicative of his indomitable attitude.
7 - Jack Wilshere was fouled today the joint-most times of any player in any Premier League game this season. Bruised.— OptaJoe (@OptaJoe) January 13, 2013
Often, Wilshere would pick up the ball deep in his own half, run about 40 yards and make a key pass to a teammate in Manchester City's third. He simply imposed himself on the game.
Santi Cazorla: 6
Of the many players in Arsenal's squad that need a rest, Cazorla is most desperate.
The Spaniard was not nearly as involved in the Gunners' attacking play as he usually is. Perhaps that was a function of Arsenal not attacking as much as they usually do, but Cazorla is eminently capable of changing a game.
He could have done so with a couple good opportunities outside the box, but failed to hit the target once.
Alex Oxlade-Chamberlain: N/A
Hauled off after Koscielny's red card to make way for Per Mertesacker. The Ox only lasted a dozen minutes.
Lukas Podolski: 6
I can't remember Lukas Podolski getting involved in the game all that much, but he didn't have a lot of time to do so.
Substituted after 57 minutes, the German made two notable contributions to the game. The first was conceding the free-kick that led to James Milner's goal, and the second was getting off a rare shot on target with a quick strike off Joe Hart's hands.
Other than that, a fairly uneventful, if physically taxing day for Podolski.
Theo Walcott: 4
Manchester City's defense was to be the sternest and most reliable test of Theo Walcott's ability to play as a central striker. So after a 90-minute exam, how did Walcott do?
A resounding failure.
As stated above, he had fewer touches of the ball than Olivier Giroud, despite playing the full 90 minutes. Completely neutralized by Vincent Komany and Co., Walcott was anonymous for much of the match, although he had a late shot cleared off the line by Joleon Lescott.
It would have been interesting to see who Arsene Wenger chose to start at striker if Olivier Giroud was fully fit, but now that he is, the Frenchman should unquestionably be first-choice.
If anything underscored the need for Arsenal to bring in reinforcements this month, it was Walcott's performance.