Luis Garcia fired Liverpool past Chelsea and into the European Cup final for the first time in 20 years.
They led inside four minutes when Milan Baros beat Petr Cech to the ball and Luis Garcia tapped in, despite Chelsea claiming it did not cross the line.
Liverpool's defence did the rest as they withstood everything Chelsea's ineffective attack could throw at them.
Chelsea's best chance came deep into injury time but Eidur Gudjohnsen thrashed a volley just wide.
After drawing 0-0 in the first leg at Stamford Bridge, Liverpool knew they needed a goal, but even they could not have envisaged doing it so early.
John Arne Riise started the move by cutting in from the left and finding Steven Gerrard, who played a first-time flick with the inside of his right foot.
The pass fell perfectly for Baros, who knocked it over the onrushing Cech and went down under the challenge from his international team-mate.
Luis Garcia was left to add the finishing touch, despite William Gallas' attempts to clear off the line.
Blues manager Jose Mourinho would later claim it had not crossed the line, but with television replays inconclusive, any argument was academic.
Reds boss Rafael Benitez was unwilling to say whether he thought the ball had gone in.
Not that the Spaniard had to - by then he knew he had added another glorious chapter to his new club's rich history books.
After that goal the expected Chelsea onslaught never materialised, with the newly-crowned Premiership champions enjoying the bulk of possession but surprisingly devoid of any sort of attacking invention.
Chelsea threatened only once in the first 45 minutes when Frank Lampard dispossessed Luis Garcia and fed Joe Cole, who lobbed over Jerzy Dudek but also wide of the mark.
The second half started in similar fashion, with Gudjohnsen shooting high and wide from 35 yards as Chelsea's efforts became desperate.
Lampard finally called Dudek into action with a powerfully-struck free-kick that the Polish keeper got down well to palm away for a corner.
Mourinho responded by bringing on Marteja Kezman for Tiago and introducing Arjen Robben for the disappointing Cole.
Robben threatened an equaliser that would have sent Chelsea through on 74 minutes, but his shot from inside the box was blocked by the outstanding Jamie Carragher.
Moments later he shot over as the Blues finally showed signs of life.
With seven minutes to go Robben found space on the left to fire in a dangerous cross that neither Drogba nor Kezman could get on the end of.
The late drama was heightened when the fourth official indicated six minutes of injury time.
Djibril Cisse could have made the game safe when he broke free but was denied a second goal by Cech.
With over 95 minutes on the clock Chelsea's best chance of the game fell to Gudjohnsen after Dudek had came to punch and failed to clear, but he volleyed wide from close range.
Liverpool: Dudek, Finnan, Carragher, Hyypia, Traore, Hamann (Kewell 72), Biscan, Luis Garcia (Nunez 84), Riise, Gerrard, Baros (Cisse 59).
Subs Not Used: Carson, Smicer, Warnock, Welsh.
Goals: Luis Garcia 4.
Chelsea: Cech, Geremi (Huth 76), Ricardo Carvalho, Terry, Gallas, Tiago (Kezman 68), Makelele, Lampard, Cole (Robben 68), Drogba, Gudjohnsen.
Subs Not Used: Cudicini, Johnson, Forssell, Nuno Morais. Agg (1-0)
Ref: Lubos Michel (Slovakia).