Jack Marriott came off the bench to score twice for Derby, including an 85th-minute winner in a pulsating encounter in which both teams were reduced to 10 men.
With Aston Villa awaiting the winners, Derby, managed by former England and Chelsea midfielder Frank Lampard, became the first team to turn around a first-leg home defeat in the playoffs, which provide the final promotion spot to England's top flight.
Leeds took the lead in the 24th minute when Kalvin Phillips launched a free kick into the box which bounced through the area and out off the post with Stuart Dallas reacting well to slot the ball home from close range.
That put Leeds 2-0 up on aggregate but just before the break, a terrible defensive mix-up between Leeds keeper Kiko Casilla and defender Liam Cooper allowed Derby substitute Marriott to convert into an empty net with his first touch of the game.
A minute after the interval Mason Mount put Derby 2-1 up with a fine finish after a clever touch from Harry Wilson, who then made it 3-1 on the night with a 58th-minute penalty.
Derby were attacking with pace and invention and scrapping for every ball in midfield but Leeds, managed by Argentine Marcelo Bielsa, were able to get back on level terms on aggregate with a fine effort from Dallas.
He cut in from the left and fired home a diagonal drive in the 62nd minute.
Leeds went down to 10 men though in the 78th minute after Gaetano Berardi was dismissed after a second yellow card for a late lunge on Bradley Johnson.
That gave Derby the belief to push for the decisive fourth goal with Wilson hitting the post in the 84th before Marriott grabbed the decider moments later with a clinical finish after good work from Richard Keogh.
Derby's celebrations were dampened slightly, however, by Scott Malone's red card in stoppage time, ruling him out of the final.
Lampard, who will come up against his former Chelsea team mate John Terry, who is assistant coach at Villa, hailed the approach of his players.
"I said to the lads that everyone had written us off. We changed the system and made a little tweak. But we needed the lads to show bravery on the ball and they did," he said.
"The goal before halftime gave the players belief and I am so delighted for Jack Marriott. I felt it was his night but I didn't know he'd do that. We have to enjoy the moment but now prepare for Aston Villa, but we'll be underdogs again," he said.
The final will be played at Wembley Stadium on May 27.
(Reporting by Simon Evans; Editing by Toby Davis)
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