Ben Watson scored the shock winner in the last minute of the match to secure a famous triumph.
Wigan must now focus quickly on the Premier League, with two games left to save their status in the top flight.
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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.