The Gunners were forced to play with a man disadvantage for 80 minutes after Laurent Koscielny was sent-off for hauling down Edin Dzeko in the penalty area - although the Bosnian striker missed the resulting penalty.
City made their man advantage count with two first-half goals as James Milner fired an excellent opener from a tight angle before Dzeko did manage to get his name on the scoresheet with close-range tap in.
Both teams were then forced to play the final 15 minutes with 10 men after City captain Vincent Kompany was also sent-off for a two-footed challenge on Jack Wilshere.
Under pressure after Manchester United’s 2-1 victory over Liverpool earlier in the day had temporarily extended the gap at the top of the table to 10 points, second-placed City responded to their bitter rivals in impressive style while Arsenal remain sixth in the Premier League, six points adrift of the top four.
City returned one third of their allocation of 3,000 tickets as fans baulked at the £62 admission cost - but those who did splash out were treated to an historic victory as they recorded their first league win at Arsenal in 38 years.
Roberto Mancini’s side took control of the game as Arsenal understandably toiled with 10 men against the reigning Premier League champions. In the end, it was a routine victory as City exploited the extra space with classy passing and movement before seeing out the victory in the second half.
On a freezing day in north London, Arsenal made four changes to the side that drew 2-2 in the FA Cup clash against Swansea as Thomas Vermaelen, Lukas Podolski, Alex Oxlade-Chamberlain and Abou Diaby - after three months out with a thigh injury - returned to the starting line-up.
For City, Joe Hart and Matija Nastasic returned while Carlos Tevez was again paired up front with Dzeko with Sergio Aguero still sidelined through injury.
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While the decision infuriated Arsene Wenger and the home crowd - who hurled abuse at Dean throughout the game - the official had no choice after Koscielny elected to rugby tackle Dzeko in the penalty area as the City striker attempted to turn and shoot.
Yet Arsenal were not punished immediately amid bizarre scenes. Dzeko stepped up himself to take the spot kick, which was saved by Wojciech Szczesny with his legs before the ball rebounded off the post and across the goal-line into the goalkeeper’s arms.
City, however, dominated possession and made their man advantage count in the 21st minute with a beautifully worked opener. David Silva was alert enough to take a quick free-kick before Tevez slipped a delightful pass to Milner, who smashed his finish into the far corner from a tight angle via the post.
In the 32nd minute, the game was effectively over as a contest as Dzeko did find the net. Milner whipped in an excellent low cross from the right and the forward was on hand to tap home his 10th league goal of the season after Szczesny saved Tevez’s initial effort.
The Premier League champions nearly went three ahead before the break but Wilshere was alert to clear Javi Garcia’s header off the line from a corner.
After the break, City went into cruise control as they looked to save their energy and coast to victory. Dzeko headed just off target shortly after the re-start while Tevez was thwarted by Szczesny as he ran through on goal.
Arsenal showed fighting spirit in the second-half and were given hope in the 75th minute when Kompany was dismissed for a two-footed lunge on Wilshere. The Belgian clearly won the ball but Dean took action after ruling that the tackle was dangerous.
It made little difference as City saw out the result to repay the travelling fans and keep the pressure on United.