Dougie Freedman threw Leeds a promotion lifeline deep into stoppage-time after Carlisle had stolen a two-goal advantage in the first leg of their Coca-Cola League One play-off semi-final.
Danny Graham and Marc Bridge-Wilkinson had stunned another full house at Elland Road with goals in each half to give Carlisle a big advantage.
But on-loan Crystal Palace striker Freedman latched onto Paul Huntington's long ball into the box and forced the ball home in the fifth minute of time added on to give Leeds - second best for long periods - a fighting chance.
Graham knew little of his first-half opener when Simon Hackney's volley deflected off the Carlisle striker's backside and beyond wrong-footed Leeds goalkeeper Casper Ankergren into the net.
Bridge-Wilkinson converted Evan Horwood's cross in more emphatic fashion at the far post seven minutes after the interval to give John Ward's side a commanding two-goal cushion.
Carlisle had won only one of their last eight league matches, while Leeds had taken 18 points from their last seven, but the Cumbrians harried and pressed, outpassed and outmanoeuvred their more illustrious rivals to put themselves in the driving seat for a place in the Wembley final.
Leeds were roared on by a second successive sell-out crowd of 36,297 - but Carlisle almost silenced the home fans in the eighth minute when Graham's whipped-in cross was met first time by Bridge-Wilkinson, whose eight-yard volley hit the outside of Casper Ankergren's left-hand post.
Leeds launched a swift counter-attack three minutes later and would have taken the lead had it not been for Keiren Westwood's one-handed save that denied a curling 25-yard effort from Freedman.
The on-loan Crystal Palace striker went close again with a lob from the edge of the penalty area, but not before Ankergren tipped away Graham's header from Bridge-Wilkinson's cross.
Jermaine Beckford's curling effort was pushed away at full stretch by Westwood, but Carlisle stunned Elland Road less than 60 seconds later.
Leeds made a mess of clearing a corner and the ball fell invitingly to Simon Hackney, whose volley from the edge of the area took a decisive deflection off Graham before skidding passed the flat-footed Ankergren and into the net.
Westwood ensured Carlisle held their slender advantage just before the break with another smart save.
Neil Kilkenny's quick free-kick sent Beckford clear and his shot was smartly parried by the visitors' impressive goalkeeper.
Leeds looked all at sea immediately after the restart and could have fallen further behind when Jonathan Howson was caught in possession on the edge of his area and Ankergren blocked Bridge-Wilkinson's stinging shot.
A jittery Leeds defence survived that scare, but were cut to shreds in the 51st minute.
Hackney released Horwood on the overlap down the left and the full-back's low cross was turned home at the far post by Bridge-Wilkinson without a white shirt in sight.
Tresor Kandol replaced an unhappy Beckford just before the hour-mark and saw his header at full stretch tipped over by Westwood in the 69th minute - but still Leeds struggled to find their range.
Leeds had two penalty appeals turned down in the space of a few minutes, the first more vociferous when the ball appeared to strike a Carlisle arm in the box and the second when Freedman went tumbling in the box under Peter Murphy's challenge.
Paul Huntington's shot on the turn was blocked by Westwood in the closing stages and Kandol was denied by the Carlisle goalkeeper soon after - but Freedman pounced on Huntington's ball forward in the dying seconds, giving Leeds hope for Thursday's second leg.
Leeds United (4-4-2): Ankergren; Richardson, Huntington, Michalik, Johnson; Kilkenny, Douglas, Howson (Hughes, 90), Prutton (Carole, 78); Freedman, Beckford (Kandol, 58). Substitutes not used: Lucas, Marques.
Carlisle United (4-5-1): Westwood; Arnison, Murphy, Livesey, Horwood; Dobie, Bridge-Wilkinson, Lumsdon, Smith (Thirlwell, 80), Hackney (Taylor, 69); Graham (Madine, 90). Substitutes not used: Howarth, Campion.
Referee: A Bates (Staffordshire).