The Gunners went into the game coming off the back of a superb 3-0 win over Stoke City last weekend, and continued their form with a surprise win over City.
Manuel Pellegrini's men drew last weekend against Everton and didn't look any more convincing today, and now slip five points behind league leaders Chelsea after this draw.
Arsenal were the better side throughout, and took the lead after 24 minutes, with left back Nacho Monreal drawing a challenge from Vincent Kompany to win a penalty for Arsene Wenger's side.
In-form Santi Cazorla stepped up to put the ball into the back of the net, and the Gunners seemed to grow in confidence as time wore on - a change from Arsenal's usual performances against in the 'big' games.
Cazorla was sublime throughout and unsurprisingly had a hand in the second goal too, crossing in a superb free kick for Olivier Giroud to head home and wrap the game up.
Arsenal move fifth, just one point behind fourth placed Manchester United, whilst a lethargic City need to find answers for today's poor performance - or face being left behind by Chelsea.