City, one of Europe's top teams, was looking to avenge its shock defeat to Wigan in last year's final but slumped to a 2-1 loss at home, ending its hopes of a domestic treble just seven days after winning the League Cup final.
"People kept saying we were lucky last year," Wigan captain Emmerson Boyce said, "but we're going back to Wembley and we're making history again."
Wigan can seal a return to the final against all the odds by beating Arsenal, which is now overwhelming favourite for the competition. The other semifinal will be between Hull - which is into the last four for the first time since 1930, and Sheffield United - which became the first third-tier team to reach the semifinals since 2001.
Hull defeated Sunderland 3-0 and United scored twice in two minutes to beat Charlton 2-0.
"To get to this stage as a League One club in the semifinal is an incredible achievement," said United manager Nigel Clough, the son of late English coaching great Brian Clough.
Arsenal, which advanced on Saturday with a 4-1 win over Everton, won't have a better opportunity to end its nine-year trophy drought. But the Gunners will underestimate Wigan at their peril.
City did just that by fielding a raft of second-string players with Wednesday's Champions League match against Barcelona in mind, and they paid a huge price.
"It's disappointing because we cannot be eliminated from the FA Cup at home by Wigan," City manager Manuel Pellegrini said.
Wigan's players threw their shirts into the crowd and took in the adulation of their fans after pulling off a tactical triumph for its manager Uwe Rosler, an East German who spent four years at City from 1994-98 and became a cult hero at the club.
Jordi Gomez converted a 27th-minute penalty after Martin Demichelis fouled Marc-Antoine Fortune and James Perch tapped in Wigan's second in the 47th.
City couldn't reproduce the comeback it delivered against Sunderland in last weekend's League Cup, with Samir Nasri's 68th-minute goal its only reply.
"We pressed them high, got in their faces and they didn't like it," Perch said. Anything is possible now. Hopefully we can prove a few people wrong again in the semifinal against Arsenal."
Sunderland also missed the chance for a quick return to Wembley as Hull scored three second-half goals after having a penalty saved before halftime.
Hull captain Curtis Davies rose highest in the 68th to head in Tom Huddlestone's free kick, before David Meyler supplied a cool finish four minutes later after chasing down a punt upfield. Lee Cattermole played a shocking back pass that left the lurking Matty Fryatt with the simplest of chances to score just minutes later.
The semifinals will be played on April 12-13.Suggest a correction