Roberto Martinez’s side are 21 points below Everton in the top-flight, but they made a mockery of that gap with a stunning first half goal-spree in the last eight at Goodison Park.
Wigan’s previous best Cup run saw them eliminated in the 1987 quarter-finals, but they finally bettered that effort thanks to three goals in three minutes from Maynor Figueroa, Callum McManaman and Jordi Gomez.
It will be an emotional return to Wembley, which stages both semi-finals, for Wigan owner Dave Whelan, who broke his leg while playing for Blackburn against Wolves in the 1960 Cup final.
The only disappointment for Wigan was an injury to Japanese midfielder Ryo Miyaichi, who was stretchered off in the closing stages after a strong challenge from Kevin Mirallas.
David Moyes’ men were first to threaten when Mirallas whipped in a dangerous cross that Sylvain Distin met with a glancing header which flew just wide.
The Latics are once again firmly embroiled in a fight to avoid relegation, but they were quickly into their stride and Shaun Maloney went close with a curling shot from the edge of the area that beat Everton goalkeeper Jan Mucha, only to rebound to safety via the far post.
Arouna Kone had scored in both league meetings with Everton this season and he should have added to that tally with a close-range header that looped over.
Nikica Jelavic drilled in a shot on the turn that Joel Robles saved well, but Wigan’s reserve goalkeeper would rarely be tested after that.
Mucha, standing in for the injured Tim Howard, had to produce a splendid save to keep out James McCarthy’s stinging half-volley from 20 yards.
But Mucha was helpless to prevent Wigan taking the lead in the 30th minute when Honduras defender Figueroa, escaping Leon Osman’s attempt to mark him, powered in a header from Gomez’s corner.
Everton were stunned by that setback and Phil Neville seemed especially troubled as he gifted Wigan their second goal just one minute later.
Instead of picking out a team-mate, Neville misplaced his pass from the halfway line into the path of McManaman, and the boyhood Everton fan took full advantage, surging clear on goal before planting a cool finish past Mucha.
Wigan completed their astonishing spree two minutes later with the best of the bunch as a flowing move left Moyes’s side leaden-footed before Gomez caressed a brilliant strike past Mucha from the edge of the penalty area.
Moyes sent on Victor Anichebe in place of Neville at half-time, but Everton struggled to build any sustained momentum.
And the fans’ frustration boiled over as they jeered Marouane Fellaini when Everton’s star midfielder was substituted after a lacklustre display.
The home side’s hopes of a late fightback were dashed when a Mirallas strike was correctly ruled out for offside.