The home side surged into a two-goal lead thanks to record signing Nathan Ellington and never looked back despite an anxious last five minutes when Fulham finally breached the Wigan rearguard.
Ellington struck first on 20 minutes with a low drive after a delightful back-heel from Welsh international Neil Roberts had created the opening.
And eight minutes later 'The Duke' doubled the home side's lead when he pounced on a throughball from the impressive Stephen McMillan to fire past the stranded Maik Taylor.
The Londoners finally came alive in the last quarter and substitute Luis Boa Morte had Wigan hearts fluttering when he pulled a goal back five minutes from time, but the home side held on and will now host holders Blackburn Rovers in the quarter-finals.