Chelsea came from 2-0 down with 10 men to reach their second Champions League semi-final in sensational fashion.
Sergio Busquets gave the Catalans the lead in the 33rd minute before John Terry was sent off for kneeing Alexis Sanchez in the back.
Lionel Messi then assisted Andres Iniesta to double the Blaugrana lead, but Brazilian midfielder Ramires executed a marvellous chip on the stroke of half-time to put Chelsea ahead in the tie on away goals.
Early in the second-half, Didier Drogba fouled Cesc Fabregas to concede a penalty, but World Player of the Year Lionel Messi smashed the crossbar and personally struggled for the remainder of the match afterwards.
A fabulous rearguard display from the Blues, adopting their Italian manager's catenaccio blueprint, frustrated a pedestrian and fraught Barca who appeared to have no plan B.
With three minutes of extra-time signalled, substitute Fernando Torres latched on to a hoofed clearance from Ashley Cole to round Victor Valdes and equalise, taking Chelsea ahead in the tie and giving them the cushion of a second away goal.
Di Matteo will be without not only Terry, but Branislav Ivanovic, Ramires and Raul Meireles for the final after the trio all picked up second bookings in the tournament, meaning a one-match suspension.
Gary Cahill's season could be in doubt too after he appeared to pull a hamstring when stretching for the ball in the opening minutes of the match.
Portuguese David Luiz will start the 19 May final against either Bayern Munich or Real Madrid, providing he regains fitness in time for the Munich event.
Avid tweeter Juan Mata couldn't contain his joy:
A sheepish Terry, who initially claimed he did not deliberately knee Chilean Sanchez, apologised for his rashness in a post-match interview with Sky Sports' Geoff Shreeves.
"It does look bad on the replay. I raised my knee but hopefully the people out there who know me, know I'm not that kind of player.
"I feel as though I let them (team-mates) down. I have apologised to them and I apologise to the Chelsea fans. At the time I was bewildered, but looking at the replay it looks a red card. On a personal note, of course (it hurts I miss the final). But we deserve to be in the Champions League final. I really hope that doesn't take away from this win."
The Chelsea captain will be banned for three European matches, and Frank Lampard now looks set to skipper the team in their second Champions League final.
But it will be difficult to take the gloss off of a performance which arguably outranks Manchester United's comeback from two down against Juventus in Turin in 1999.
Chelsea's Herculean effort has ensured a second European Cup final in the club's history, and they have under a month until they get their chance to exorcise the ghost of Moscow 2008.