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The first chance of the game fell to the visitors as Jack Wilshere picked up a cross into the box near the far post, but smashed his volley wide.
City capitalised from the miss, immediately winning a corner at the other end of the pitch, which Sergio Aguero volleyed in from a tight angle at close range.
Vincent Kompany set up Alvaro Negredo as the home side looked to increase their advantage over the league leaders, but Nacho Monreal made it difficult for the striker, who eventually sliced his finish wide.
Against the run of play, the Gunners were able to get themselves back on level terms as Theo Walcott unleashed a hopeful strike from the edge of the box, but a possible deflection from the head of Martin Demichelis seemed to confuse Costel Pantilimon in the Man City goal to let the effort in.