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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.