A goal up from the first leg and then also ahead on the night thanks to Stuart Dallas’ strike midway through the first half, the Elland Road club’s tendency to snatch defeat from the jaws of victory returned with a vengeance.
Kiko Casilla’s calamitous mistake on the stroke of half-time offered Derby County a way back into the tie that Frank Lampard’s men ruthlessly took to book a Wembley date with Aston Villa on May 27.
Jack Marriott, the beneficiary of the United goalkeeper’s schoolboy-esque blunder, netted twice. His second five minutes from time ultimately settled a thrilling tie that had kept the 36,326 crowd on the edge of their seats to the very end.
When that end came after five frantic minutes of stoppage time, every Leeds player hit the turf as if floored by a haymaker of a punch.
Every sinew of energy in their bodies had been given over not just these two ties but a demanding season only for United to suffer a play-off heartache on a par with any of their previous four failures to win promotion via this route.
What made this one so hard to take was just how comfortable Leeds had seemed before Casilla’s rush of blood.
Wembley felt so close. So close, in fact, that the national stadium could almost be touched. Which maybe explains such a catastrophic moment of madness from Casilla, a former Real Madrid goalkeeper with three Champions League winners medals to his name.
As the clock ticked down towards the interval and Derby pumped one more aimless ball forward, Liam Cooper had the situation under control despite Marriott being in close proximity.
Had Casilla left his captain to deal with matters, the likelihood is the night would have taken a very different path.
Instead, the January signing from the Bernabeu raced from his area in a foolish attempt to clear a danger that had not existed a second or so earlier.
Casilla collided with Cooper, and the ball ran free for Marriott to tap into the unguarded net with his first touch.
At a stroke, the mood of the evening had changed. The air of jubilation that had met Dallas firing in the rebound on 24 minutes after Cooper’s header had struck the post had suddenly been replaced by a sense of foreboding.
With good cause, too, as the tie was level just 40 seconds into the second half. Richard Keogh found Wilson, who held on to the ball just long enough for Mason Mount to skip past him on the overlap.
A couple of touches to control the ball and a deft finish then sent the 2,670 travelling fans into raptures, as the rest of Elland Road looked on in stunned silence.
United’s night - and, by definition their season - took another turn for the worse just before the hour. Neat play on the edge of the penalty area saw the ball played to Bennett.
Cooper stuck out an arm, clearly impeding the Rams forward and referee Anthony Taylor rightly pointed to the spot. Wilson then did the rest from 12 yards by sending Casilla the wrong way.
Leeds, behind in the tie for the first time, needed a response and fast. Step forward Dallas, who after collecting a pass from Klich wide on the left cut inside and drilled a low shot past Kelle Roos.
With the noise levels having been restored to ear-bleeding levels, suddenly this felt like United’s tie to win.
Instead, Bielsa’s side pressed the self destruct button once again. This time, Gaetano Berardi was the guilty party.
Having survived a couple of crude hacks at his legs in the centre circle and heard no whistle from Taylor, the United defender decided to dispense his own form of rough justice via a kick at Tom Lawrence.
Berardi punched the tunnel on his way off but the real damage had been done to United’s hopes of reaching Wembley.
Five minutes from time, Marriott was played clear and he dinked a deft shot over Casilla to put the Rams back in front on aggregate.
There was still time for Scott Malone to receive his marching orders for a foul on Pablo Hernandez that means the former Huddersfield Town full back will miss the Wembley final.
But there was to be no reprieve for Leeds and their dejected supporters, who next season will be heading to the match along Kenilworth Road and not Anfield Road as hoped.
Leeds United: Casilla; Ayling, Berardi, Cooper, Dallas; Phillips; Hernandez, Shackleton, Klich (Clarke 86), Harrison; Bamford (Brown 87). Unused substitutes: Peacock-Farrell, Jansson, Struijk, Gotts, Bogusz.
Derby County: Roos; Bogle, Tomori, Keogh, Malone; Johnson, Wilson (Cole 90), Holmes (Marriott, 44), Mount; Lawrence, Bennett (Huddlestone 59). Unused substitutes: Carson, Jozefzoon, Evans, Knight.
Referee: Taylor (Cheshire).