The Blues looked like they had done enough to seal their return to the final for the second successive season after Michael Essien's ninth-minute volley had illuminated the early stages of the semi-final second leg at Stamford Bridge.
Another meeting with Manchester United was within touching distance when Iniesta popped up in added time with a stunning equaliser to level the tie 1-1 on the night and also on aggregate.
The Spain midfielder's 18-yard strike - Barcelona's first on target on a night where their front players failed to shine - sealed their passage on the away goals rule after the first leg last week had ended goalless.
Chelsea were furious at full-time as the referee had denied them several penalty appeals throughout the match and an irate Didier Drogba had to be escorted off the pitch after protesting wildly in the direction of the Norwegian official.
The late drama overshadowed a tense game which Essien had lit up with a thunderous volley on nine minutes.
The ball looped up to the Ghana midfielder off Yaya Toure and he lashed a 25-yard left-foot volley into the back off the net via the crossbar to start Stamford Bridge rocking.
With 25 minutes of the clock, Drogba was left beating the turf when he went to ground under challenge from Eric Abidal but the referee waved play on.
Chelsea were further aggrieved three minutes later when Daniel Alves tugged back Florent Malouda but the referee awarded a free-kick on the edge of the penalty area instead of a spot-kick.
Barcelona just couldn't click in the attacking third despite bossing possession and out-passing Chelsea for vast periods of the game as the Spanish side clearly struggled to cope without injured striker Thierry Henry.
But Chelsea should have been out of sight in the 55th minute when Drogba dummied Gerard Pique but saw his shot back across goal from eight yards saved by the legs of goalkeeper Victor Valdes.
Barcelona had their own reasons to feel aggrieved with the referee when he sent off Abidal after 66 minutes.
The full-back was adjudged to have clipped the heels of Nicolas Anelka as the last man when replays showed the striker looked to have gone to ground under his own steam.
Another Chelsea penalty appeal fell on deaf ears on 82 minutes when Anelka's neat flick clearly struck the hand of Pique in the box.
Barcelona then dominated the closing minutes without ever really threatening Petr Cech's goal.
But Chelsea celebrations turned to despair in the second of four minutes of added time when Essien made a hash of a clearance and Messi squared the ball to Iniesta, who smashed home a superb shot from the edge of the box past the helpless Cech.
The full-time whistle brought angry protests from the Chelsea players, but it will be Barcelona and not they who will be facing Manchester United in Rome later this month.