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Danny Welbeck came within inches of opening his account for his new club, beating Hart with a chip, only to see the ball come back off the post and into the Man City keeper's hands.
Hart was called upon again a few minutes later as Welbeck pulled the ball back to Ramsey, but the Welshman's drilled effort was straight to the keeper.
The visitors began to look more threatening as the half-hour mark approached, with James Milner trying a 25-yard effort, but it was Aguero who broke the deadlock by guiding the ball in from a well-placed Jesus Navas pass.
Arsenal pushed to get back on level terms, but Alexis Sanchez curled the ball wide from a free kick before Ozil blasted the ball well high from the edge of the box.