The Blues went into the clash 1-0 ahead but Sergio Busquets restored parity in the tie after 35 minutes, moments before Chelsea captain John Terry was shown a straight red card for a petulant knee into Alexis Sanchez’s back off the ball to put his side firmly under the cosh.
Andres Iniesta doubled his side’s lead on the night and looked to have sunk the visitors, only for Ramires to execute an exquisite lob and give his side the ascendancy once more on the stroke of half-time.
Barcelona's talisman Lionel Messi missed a penalty following the restart after Cesc Fabregas went down in the box and the Argentine maestro struck the woodwork late on as he drove a low shot against the post, but Pep Guardiola's men could not find the goal they needed to avoid going out on the away goals rule.
The match was put beyond doubt by substitute Fernando Torres, who scored in stoppage-time to break Barcelona hearts and secure a stunning 3-2 aggregate win to put Roberto Di Matteo’s side through to the Champions League showpiece in Munich.
Messi, who has plundered a staggering 63 goals in all competitions this season, had been suffering from a gastric problem and missed training on Sunday but started, while Dani Alves only made the substitutes' bench as coach Guardiola made two changes from the side that lost in London, with Gerard Pique and Isaac Cuenca drafted in. For Chelsea, Di Matteo was able to pick Didier Drogba despite the striker missing Saturday’s match against Arsenal with a knee injury.
Messi, whose seven previous games against Chelsea had not yielded a single goal, could have scored in just the third minute as he was played in down the right of the visitors’ penalty area by Sanchez, but he could only find the side netting with his shot.
Di Matteo made an enforced change after just 11 minutes as Gary Cahill slipped inside the Chelsea box and pulled his hamstring with Jose Bosingwa coming on in a defensive reshuffle. Minutes later, Pique, Victor Valdes and Drogba all landed heavily after colliding, challenging for a high ball, with the defender having to be replaced by Alves and taken to hospital for checks. Barca later confirmed that Pique suffered a concussion.
Branislav Ivanovic received a yellow card in the second half which leaves the defender suspended for the final, along with Ramires, Raul Meireles and Terry while the extent of Cahill's injury has yet to be fully assessed.
Chelsea, who were previously unbeaten in their last six Champions League games against Barcelona, almost fell behind in the 19th minute as Messi played a pair of slick one-twos, first with Sanchez then with Fabregas, before drilling a low shot on target that Petr Cech saved instinctively with his feet.
Drogba carved out a half-chance with a marauding run and shot into the side netting, but it was all but a fleeting foray as Barcelona stamped their authority on the match in the 35th minute.
Drogba half-cleared the corner, but Chelsea were not able to collect the resulting loose ball and Cuenca sped down the right before squaring the ball to Busquets, who netted only his second goal in two years from close range.
Two minutes later Chelsea’s captain made his side’s challenge all the more difficult. He pointlessly and petulantly kneed Sanchez in the back off the ball, the offence spotted by the referee’s assistant who ensured that the defender received his marching orders.
Chelsea’s misery was compounded two minutes before half-time as a buoyant Barcelona exploited the visitors’ now threadbare defence with Messi and Sanchez combining to good effect before Iniesta timed his run to perfection and beat Cech with a clinical finish.
But just moments after receiving a booking which would have ruled him out of the final, the ebullient Ramires latched on to a through ball from Frank Lampard before lobbing Valdes with an exquisite finish in added time as the keeper flew off his line.
Within minutes of the restart, Fabregas went down inside the Chelsea box under a challenge from Drogba, and the Turkish referee Cuneyt Cakir pointed to the spot for what was a hotly-disputed spot kick.
Messi stepped up to take the penalty and end that goalless run against the Blues, but his fierce shot clattered against the crossbar and the visitors had a big reprieve with the advantage still theirs. Justice was probably done, however, as replays strongly suggested that Fabregas had dived.
Messi was clearly desperate to atone for his wastefulness and combined with Alves after the hour mark to cut the defence open before Cech made a magnificent stop at the feet of Cuenca, smothering the ball with a goal seemingly certain.
Chelsea continued to look dangerous at the other end, however, and the inspired Ivanovic planted a free header agonisingly wide from inside the Barcelona box as Lampard picked him out perfectly from a corner out on the left.
Both managers made changes as they turned to fresh legs, and one such replacement Salomon Kalou lacked conviction when he was put through on goal by Lampard, as he dallied in the final third.
A scrappy and one-sided final period ensued with Barcelona desperately searching for an elusive third goal, and it so nearly came in the 83rd minute as Messi cut inside with an incisive run before driving a low shot against the near post with Cech beaten once more.
But the stage was set for substitute Torres, who found himself in yards of space and unmarked some 40 yards out with just Valdes to beat after being released in a clinical counter-attack. The £50 million striker calmly rounded the Barcelona keeper and slid the ball into the empty net to send the travelling supporters into delirium.
Chelsea sealed their place in the Champions League showpiece on May 19, against all the odds, and will now await the winner of Wednesday's match between former boss Jose Mourinho’s Real Madrid and Bayern Munich. Whatever happens in next month's final, however, Chelsea fans will always remember what was undoubtedly one of the greatest nights in the club's history.