A stunning first-half volley from Michael Essien looked to have earned Chelsea victory and set up a repeat of last year's Champions League final against Manchester United.
But Andres Iniesta beat Petr Cech in the third minute of added time to send the Spanish bench and their fans delirious and leave Guus Hiddink crestfallen.
At the final whistle, Chelsea's players confronted referee Tom Ovrebo, who had waved away at least four penalty appeals during the game.
The scenes descended into anger when Drogba emerged from the tunnel to confront the Norwegian official and was shown a yellow card.
Ovrebo had a poor game and was marshalled down to the tunnel by Chelsea stewards as Drogba continued to complain about his performance.
The Ivorian then vented his fury by shouting "it's a f***ing disgrace" down the lens of a TV camera, and the fall-out from Drogba's behaviour may yet be met by a UEFA investigation.It had all looked so promising for Chelsea when Essien, who missed six months of the season while he recovered from a serious knee ligament injury, despatched a 20-yard volley beyond the despairing Victor Valdes.
Chelsea's collective desire to reach the final once more was epitomised in the way they took the fire out of Barcelona's early football.
The Catalans, missing their two first-choice centre-backs through injury and suspension, played some neat, fast and accurate football in the first 20 minutes.
It was a perfect example of the beautiful game mastered by coach Pep Guardiola but it lacked the cutting edge in the absence of the injured Thierry Henry.
The Barca attack has shared more than 90 goals between them this season but Chelsea managed to prevent them scoring in 180 minutes of high-tempo football.
That Chelsea scored with their first real attack of the game would have left the Barca coach bitterly disappointed.
Frank Lampard's attempted cross cannoned off Yaya Toure and Essien despatched his volley into the net via the underside of the crossbar.
It sparked Chelsea into life and, for the remainder of the opening half, they bossed the game.
Lampard almost put Drogba through in the 22nd minute but Valdes managed to beat the Ivorian to the ball on the edge of the penalty area.
Barca were rocking now and a catalogue of fouls by Dani Alves was finally punished with a yellow card when he brought down Ashley Cole. It meant the full-back was out of the final.
But Ovrebo waved away penalty appeals from Chelsea when Drogba, a colossus in attack all night, was brought down by Eric Abidal.
The second half promised more drama and it did not disappoint. Drogba missed a gilt-edged chance when Florent Malouda and Anelka put the Ivorian clear in the 52nd minute.
Somehow, Valdes got a foot to his shot to keep Barca's hopes alive.
But the Catalans were in deep trouble in the 65th minute when Abidal brought down the free-running Anelka and, as the last defender, was shown the red card.
Chelsea continued to take the initiative as Barca were reduced to long-range shots.
In the 70th minute, Valdes saved Guardiola's side again when a Lampard shot took a wicked deflection.
But two minutes later Drogba was replaced by Juliano Belletti, much to the crowd's surprise and the Ivorian's clear disapproval.
As the clock ran down, Chelsea continued to pour forward in search of a decisive second to calm the nerves but, although they had made Barcelona look very ordinary, there was a sting in the tail.
Chelsea's heroes had fought for every ball as if their lives depended on it but they allowed Iniesta too much room and, when he beat Cech from 20 yards in the 93rd minute, chaos descended on Stamford Bridge.
But there was still time for more drama when Michael Ballack's goalbound effort seemed to hit a defender's arm only for Ovrebo to wave away more appeals.
Ballack was shown the yellow card for protesting and, when the final whistle sounded, Barca celebrated in unbridled fashion while Chelsea's players began their attacks on Ovrebo.
It was an unsavoury end to Chelsea's European campaign that may yet have further repercussions for the English side.
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