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Three minutes later Benedikt Howedes headed a corner just over the Arsenal crossbar.
Thereafter, the Gunners took control of the proceedings at the Veltins Arena and went ahead in the 18th minute.
Walcott almost scored his second goal of the evening just two minutes later, but Lukas Podolski's cross from the left proved to be too high for him.
It did become 2-0 to Arsenal and the second goal came in the 26th minute, Giroud heading home Podolski's cross past Lars Unnerstall.
Schalke could have halved the deficit six minutes from the half-time interval had Jefferson Farfan been able to his shot on target.
The Dutch striker could have equalised for Schalke five minutes after the break when he shot on goal, but Mannone made a brilliant save.
The hosts had another chance to make it 2-2 in the 63rd minute when Holtby was denied by Mannone.
Four minutes later Schalke restored parity, as Farfan's shot from a Holtby cross was deflected into the Arsenal goal by Thomas Vermaelen.
The home side controlled the proceedings for the remainder of the match, but had to settle for a point.