Maynor Figueroa, Callum McManaman and Jordi Gomez scored within just 202 seconds of each other in the first half to demolish last year's semi-finalists hope of a return to Wembley.
Everton had created the first chance with Sylvain Distin heading wide but from then it was almost one-way traffic as Shaun Maloney, who caused the hosts numerous problems with his movement in from the left, curled a shot past Jan Mucha but back off the post.
The hosts' only other real chance of the first half fell to Nikica Jelavic, without a goal in two months, but his low effort was palmed away by Joel Robles.
Then the madness began as Wigan incredibly put the game beyond their opponents in the space of less than four minutes.
Mucha, making his FA Cup debut with Tim Howard sidelined by broken bones in his back, passed his first real test by turning James McCarthy's shot behind. However, from Gomez's 31st-minute corner the Slovakian got himself in a tangle inside the six-yard box and Figueroa powered home a far-post header.
If Everton looked stunned by that what followed in barely a matter of seconds left them staggered and virtually out for the count. Huyton-born McManaman, released by Everton as a 16-year-old, outsprinted Distin to expertly clip a shot past Mucha.
And while they were all still celebrating that goal Wigan made it 3-0 as Gomez fired home from 20 yards. The goal was greeted by loud boos from the majority of the crowd, who having been told Wigan would field a weakened side - they made four changes to the team which were thrashed 4-0 at home by Liverpool last weekend - saw their own dreams of a Wembley return collapsing in front of their eyes.
It is safe to assume the Everton dressing room would not have been a pleasant place during half-time with Moyes most certainly unhappy with the lack of fight his side had shown.
Although the performance improved the hosts rarely threatened and when substitute Ross Barkley blazed wide late on it ended any fanciful hopes of a dramatic comeback.