An incredible four-minute spell from the visitors sealed victory over a disappointing home side and booked their place in the last four for the first time in the club's history
Three goals in a mad four first-half minutes from Maynor Figueroa, Callum McManaman and Jordi Gomez left the hosts stunned at the break.
Everton were unable to orchestrate an unlikely comeback and Wigan's half-time lead proved enough to seal an excellent victory for Roberto Martinez's men and put them into the last four.
David Moyes decided not to risk goalkeeper Tim Howard, who was struggling with a back injury, meaning Jan Mucha took his place in goal. Meanwhile John Heitinga deputised for Phil Jagielka, who is awaiting surgery on an ankle injury.
Wigan made four changes from last weekend’s defeat against Liverpool, as Martinez threw cup shot-stopper Joel Robles in goal, while Gomez and McManaman also gained a place in the XI alongside Antolin Alcaraz, who made his first start since August.
It was a tight opening few minutes, but when Shaun Maloney managed to find space on the left he was inches away from putting Wigan in front, as he cut inside and curled a beautiful 20-yard effort around Mucha which came back out off the post.
Goal-shy Nikica Jelavic then forced a fine save from Robles, as he let the ball roll across him and fired a low effort from the edge of the box, only to be denied by the Wigan goalkeeper.
After James McCarthy tested Mucha with a rasping 25-yard volley, the Latics took the lead from the resulting corner as Figueroa rose highest at the far post to nod the ball low into the net.
Seconds later the lead was doubled when McManaman latched on to Phil Neville’s wayward pass and broke free before slotting a superb finish past the onrushing Mucha.
The madness continued just moments later as Arouna Kone squared the ball to Gomez on the edge of the box, and the midfielder stroked a delightful finish into the corner with Mucha watching helplessly, leaving the hosts in utter disarray at the break.
Moyes threw on Victor Anichebe for the disappointing Neville in the second half as Everton tried to inspire a comeback, and Fellaini almost got the hosts back in it as he volleyed an effort wide from 20 yards out.
The Toffees seemed to run out of steam midway through the second half, and even the ever-reliable Baines struggled, firing a low cross straight into the arms of Robles with several team-mates available in the box.
Substitute Ross Barkley fired a late effort just wide of the post and Osman was denied by Robles from close range, but the Latics did a good job of stifling Everton’s rhythm as they cruised to a superb victory.