Danny Tickle's drop goal three minutes from time put the Warriors into the Tetley's Super League Grand Final for the fifth time.
In a thrilling game at Headingley, Mike Gregory's side came from 14-4 down to become the first team from outside the top two to reach Old Trafford.
They will take on Bradford in the final on 18 October, keen to avenge their 37-6 battering by the Bulls in 2001.
Tickle's kick proved crucial but it was two spectacular long-range tries from Brian Carney that set the platform for a tremendous win.
His first opened the scoring, the Irish winger fielding Andrew Dunemann's kick inside his own 20-metre area and scything through the wide open spaces before taking a return pass from Kris Radlinski to touch down.
Danny McGuire, chosen ahead of Mark Calderwood, hit back for Leeds, racing on to Matt Diskin's grubber kick to touch down for the equalising try.
Skipper Kevin Sinfield kicked the conversion and added a penalty to make it 8-4 after Quentin Pongia was pulled up for a high tackle on Chris McKenna.
The Rhinos extended their lead on 25 minutes when Ron Burrow wronged footed Tickle to scoot over for a second try.
Sinfield's third successful goal made it 14-4, but Wigan hit back just before the interval when stand-off Sean O'Loughlin forced his way over.
Warriors skipper Andy Farrell, who resumed the goalkicking duties when Tickle was substituted, added the conversion to cut the deficit to just four points.
The Rhinos extend their lead two minutes later when Burrow dived over for his second try.
But the Warriors closed to within two points when O'Loughlin crossed for his second of he night and Farrell added his second goal.
Sinfield landed a 60th-minute penalty to make it 20-16, but Carney went 80 metres for the second time to touch down.
Sinfield brought the scores level with a 75th-minute penalty but Tickle had the final say to ensure Daryl Powell's reign as Leeds coach ended on a losing note.Like