Lions midfielder Jimmy Abdou stunned a partisan full house in West Yorkshire to send the Londoners to Wembley.
The Frenchman turned home substitute Lewis Grabban's cross in the 73rd minute to silence most in the biggest crowd outside the top flight this season.
Leeds striker Luciano Becchio had bundled home a 52nd-minute equaliser to level the tie and send most of the 37,036 attendance into delirium.
Jermaine Beckford, Leeds 34-goal forward, saw a 48th-minute penalty saved by David Forde, before Argentinian team-mate Becchio appeared to have sent a nerve-jangling second leg towards extra-time.
But Abdou popped up to convert Millwall's only chance of the match and the Londoners edged through to their first play-off final at the fourth attempt.
Leeds, chasing their third play-off final appearance in four years, had spent most of the 90 minutes battering the Millwall defence, but they must endure a third season in the third tier after another sterling defensive display from Kenny Jackett's battlers.
Leeds manager Simon Grayson named an unchanged starting line-up, while Kenny Jackett recalled first-leg match-winner Neil Harris, who scored the only goal at The Den.
A super-charged atmosphere at kick-off got the better of Millwall midfielder Adam Bolder, who clattered into Robert Snodgrass in the second minute to earn the game's first booking.
Leeds' expected early charge was repelled and the home side had to wait until the 17th minute for their first shot on target when Snodgrass' low shot was comfortably gathered by Millwall goalkeeper David Forde.
Snodgrass then created a clear opening, sliding the ball through for Beckford, whose low shot was smothered by Forde.
The Millwall number one recovered to hold Fabian Delph's follow-up before another low drive from Snodgrass failed to cause concern.
Gary Alexander fired over the crossbar in the 40th minute and although that was the visitors' first shot, Millwall had accomplished all they had set out to do in a goalless first half.
Andy Robinson, a 35th-minute substitute for the injured Neil Kilkenny, snatched at a half-chance and his wayward volley was symptomatic of Leeds' anxiety.
Early in the second half Leeds were thrown a lifeline when referee Mark Halsey penalised Andy Frampton for pulling Sam Sodje.
But Beckford's spot-kick lacked conviction and Forde saved low to his right, with Robinson bundling the ball wide as he followed up.
It was a heroic effort by the visiting goalkeeper, who moments earlier had been hit by a coin thrown from the crowd despite the extra security behind the visiting goal.
But Leeds came roaring back and sent Elland Road into wild frenzy with a 52nd-minute equaliser.
Outstanding left-back Ben Parker galloped down his flank and sent in a cross that was forced home by Becchio to haul Leeds ahead on the night and level on aggregate.
There appeared no way Millwall could halt the Leeds charge, but they held on and somehow conjured an equaliser in the 73rd minute.
David Martin's deep cross was played back across the six-yard area by 65th-minute substitute Grabban and Abdou sidefooted the ball home.
The goal rocked Leeds and their fans back on their heels and for the first time the 1,000 Millwall fans, handed their tickets by Leeds officials at Woolley Edge service station prior to their arrival, could be heard.
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