Roberto Martinez's men stunned the home side as Maynor Figueroa, Callum McManaman and Jordi Gomez all found the net to end the Toffees' hopes of silverware this season and secure a first-ever semi-final place in the competition for the Latics.
The opening half-hour was an even affair with Sylvain Distin flashing a header wide and Nikica Jelavic forcing back-up Latics goalkeeper Joel Robles into a diving save, while Paul Scharner's superb tackle denied Leighton Baines.
Shaun Maloney curled a shot from the edge of the area against the inside of the post with Jan Mucha beaten, before the Everton goalkeeper had to be alert to push away a neat half-volley from James McCarthy from the edge of the area.
But from the resulting corner in the 30th minute, Wigan took the lead and never looked back, with Figueroa climbing above Leon Osman at the far post with relative ease to break the deadlock.
Everton were then complicit in their downfall as Phil Neville's horrendous pass only succeeded in releasing McManaman, with the boyhood Toffees fan bursting clear to beat Mucha with a composed finish.
And it was 3-0 moments later thanks to a sublime finish from Gomez, with the Spaniard curling a precision first-time effort from outside the box around two defenders and into the bottom corner of a static Mucha's net after Arouna Kone's astute pull-back.
Everton manager David Moyes made a change at the interval, sending on Victor Anichebe for Neville and the home side pressed forward in the second period as they searched for a route back into the contest.
Former Wigan man Baines fired a free-kick straight at Robles from long range in the 50th minute before the strangely subdued Marouane Fellaini powered a shot narrowly wide from just outside the penalty area.
Fellaini's poor pass in his own box then gifted a shooting chance to Figueroa, but the Wigan man failed to get any real power on his shot and Mucha was able to save comfortably, with the Belgium international replaced by Darron Gibson soon before heading straight down the tunnel.
The Latics suffered a blow in the 71st minute when unfortunate substitute Ryo Miyaichi, who had been sent on for the injured McManaman for his first appearance since November after a long-term absence of his own, was stretchered away with an ankle injury after a full-blooded challenge from Kevin Mirallas.
Mirallas had the ball in the net in the 75th minute, but the assistant referee's flag had long since been up for offside, substitute Ross Barkley drilled wide late on, before Osman forced a fine save from Robles in injury time and Seamus Coleman headed the follow-up wide to sum up Everton's day.
After the match Roberto Martinez was keen to savour a special afternoon in the history of Wigan Athletic.
He said: "To score three goals away from home in the manner we have done we always looked a real threat going forward and it was a complete performance and a special day for Wigan.
"I think you have to be at your very best at Goodison Park to keep a clean sheet. We played well but more importantly we had incredible concentration levels.
"You unfortunately get used to people saying if you lose it is because you are Wigan and if you win it is because the opposition was poor."
But it was a miserable afternoon for David Moyes, who admitted: "Wigan played well and on the day we didn't play well. Today was one of those days where it didn't go well at all and we just didn't perform.
"We can't argue, Wigan were the better team on the day. We can't complain, we weren't good enough.
"We never really got to grips with the game. We just didn't look as if we had the creativity which would make that happen."
|Everton||Team Statistics||Wigan Athletic|
|0||1st Half Goals||3|
|3||Shots on Target||6|
|8||Shots off Target||5|
|52.7||1st Half Poss.||47.3|
|53.5||2nd Half Poss.||46.5|