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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.