Despite missing two of their big-name signings in Robinho and Carlos Tevez, the Citizens were good value for the three points.
Manuel Almunia's bizarre own goal saw City take the lead completely against the run of play in a half which was mainly dominated by Arsenal.
Diving across to meet Micah Richards' looping header, from Gareth Barry's cross, Almunia missed the ball but it struck the post and the rebound came back off the back of the unfortunate Spaniard's head and trickled across the line.
Despite this blip Arsenal remained in control for most of the game and even stepped up a gear in the second half after the introduction of Tomas Rosicky.
The Czech midfielder helped orchestrate a well-deserved equaliser that looked like it was coming from the start.
Over an hour had passed when Robin Van Persie finally equalised when he successfully turned Joleon Lescott and fired a sweet shot across Shay Given and into the back of the net.
With the temperature and the stakes rising as the minutes ticked away it was a breakaway from Craig Bellamy that proved to be the tipping point in the game with just a little over 15 minutes remaining.
Richards had been marauding further forward in the second half and he provided a neat square pass for Bellamy to sweep into the Gunners goal.
With the crowd behind the City players, Adebayor proceeded to show off his skills by skipping past three players to cross for Shaun Wright-Phillips, who could only put the ball wide from close range.
With ten minutes to go Adebayor got his reward when Richards again provided a cross and the big striker planted a header past the helpless Almunia.
Adebayor was booked for his extravagant celebrations - performed after running towards the visiting fans.
City killed the game after Bellamy disposed Abou Diaby just outside the City area and led the charge deep into the Arsenal half, pausing only to slide the ball to Wright-Phillips who got his reward for never giving up all afternoon.
Rosicky's late goal following a lofted cross from Cesc Fabregas proved to be scant consolation for the travelling fans.