The dramatic semi-final second leg at the Nou Camp ended 2-2 and meant Chelsea, chasing a first European title, will play Real Madrid or Bayern Munich in the May 19 final with the Germans holding a 2-1 lead ahead of Wednesday's Bernabeu game.
A victory for Real would pit coach Jose Mourinho against former club Chelsea, who were in disarray just a few weeks ago.
Tuesday's match first swung Barca's way when they opened a two-goal lead through Sergio Busquets and Andres Iniesta and Terry was sent off for lifting a knee into the back of Alexis Sanchez off the ball.
The home side appeared in total control but Chelsea hit back unexpectedly when Frank Lampard sent Ramires clear in first-half added time and he lifted the ball brilliantly over the onrushing Barca goalkeeper Victor Valdes into the empty net.
Barca, who dominated possession throughout as they had done in losing the first leg in London 1-0, squandered a chance to make it 3-1 early in the second half when the referee awarded a penalty for a debatable Didier Drogba foul on Cesc Fabregas.
World Player of the Year Messi, also denied by a post late on, crashed his spot kick against the crossbar with Petr Cech beaten and has now gone eight games without scoring against Chelsea - by far his worst record against any club in Europe.
Substitute Fernando Torres, who had an impressive record against Barca when at Atletico Madrid but has repeatedly misfired for the Premier League side, then netted for Chelsea in stoppage time after racing clear and rounding Valdes.
"Football is like that, the favourite, the best team does not always win," a jubilant Torres told Spanish TV.
"We knew that was the way we had to play against Barca and often it's not the prettiest spectacle but those are our weapons," added the former Liverpool forward.
"We have a great deal of respect for Barca, for us they are the best team in the world and that's an extra motivation."
Chelsea's incredible rearguard action over the two legs is all the more remarkable given they sacked coach Andre Villas-Boas last month and Roberto Di Matteo is in charge only on an interim basis. They lie sixth in the Premier League.
"This year the league has been disappointing but now we are through to two finals," said Torres, whose side play Liverpool for the FA Cup on May 5 before heading to the Munich showpiece.
"A bad season could still turn into a memorable one."
Barca's elimination, meanwhile, is a fresh setback for Pep Guardiola's side after they crashed to a 2-1 La Liga reverse at home to Real on Saturday that left them seven points behind their bitter rivals with four games left and all-but ended their bid for a fourth straight Spanish crown.
Guardiola has led Barca to 13 titles since taking over in 2008, including Champions League triumphs in 2009 and 2011, but Tuesday's failure will inevitably lead to further speculation about the former midfielder's future.
He has yet to agree an extension to his contract beyond the end of this season and reports have suggested he might take a rest or join another club.
Chelsea, who fell to Manchester United in the 2008 final, will head to the Munich showpiece with Terry, defender Branislav Ivanovic and midfielders Ramires and Raul Meireles all suspended.
Gary Cahill, who limped off with an apparent muscle strain in the 12th minute, faces a race to be fit as does fellow centre back David Luiz, who missed Tuesday's match through injury.
"It was hard when you lose both centre halves like that," left back Ashley Cole said.
"But at the end of the day we all believed. Not many people did, but we all did.
"Three or four months ago no one thought we had a chance. We lost a few games in the Premier League. We've been lucky, but it shows you can't beat our desire and fight."
Barca, who lost Gerard Pique to concussion midway through the first half, knocked Chelsea out on away goals at the same stage in 2009 thanks to a last-gasp Iniesta strike but could not repeat the feat three years on. — Reuters