Lukas Podolski scored twice, with Theo Walcott and Aaron Ramsey netting the other goals for the Gunners as they move above Tottenham with one game remaining this season.
For their visitors, Wigan, who had won the FA Cup on Saturday and scored through Shaun Maloney, the defeat brought to an end a hugely impressive eight year stint in the Premier League.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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