The Merseysiders will face Italy's AC Milan or PSV Eindhoven of the Netherlands in their sixth European Cup final and first for 20 years on May 25 in Istanbul.
Slovakian referee Lubos Michel ruled the shot that gave them victory over the newly-crowned Premier League champions had crossed the line though TV replays were inconclusive.
Liverpool captain Steven Gerrard superbly deflected forward a square pass from John Arne Riise on the left and striker Milan Baros lobbed it over Chelsea's advancing goalkeeper Petr Cech who brought down his Czech countryman inside the area.
Garcia followed up to knock the ball goalwards and it took a slight deflection off Chelsea captain John Terry before William Gallas hooked it from under the bar.
But the goal was given -- and the Anfield side's defense stood firm in the face of Chelsea's second-half onslaught.
Keeper Jerzy Dudek made a fine diving save from Frank Lampard's 67th minute free kick as Liverpool made it through to the final.
But Chelsea manager Jose Mourinho said after the upset defeat: "The best team lost. Noboby knows if it was a goal not even the linesman.
"We are very sad with it but... they are in the final and from my heart I hope they win. This belongs to them. I dont want to criticize them.
"They played the way they want they fought a lot I have to give them credit for that. But again we are disappointed. I am still so proud of my players."
Liverpool manager Rafael Benitez said: "We have qualified for the final which means we have done a good job. When you have your supporters behind you you run a little bit more."
Chelsea meanwhile suffered the heartbreak of losing at the semifinal stage of the Champions League for the second year running after their 5-3 aggregate defeat by Monaco last season.
The London side battled to the end though and Liverpool had to soak up almost continual pressure throughout the second half.
But the nearest Chelsea came was with almost the last kick of the game when Icelandic striker Eidur Gudjohnsen fired wide from a tight angle.
A strike then after an agonising six minutes of time added on and Chelsea would have gone through on the away goal rule.
For once Chelsea coach Jose Mourinho who won the European Cup with Porto last year could not devise a plan to save his side.
The latest 'was it or wasn't it a goal?' debate will bring fresh calls for new technology to help make key decisions.
As his dream of a repeat victory died Mourinho had to accept second best to his old Spanish rival Rafael Benitez himself a European winner with Valencia in the UEFA Cup last season.
Liverpool had clearly been the better side in the first half settled by the goal and reacting to the loose ball quicker tackling harder and largely dominating a hugely competitive midfield battleground.
Although Lampard Gudjohnsen and Tiago worked tirelessly for Chelsea Didier Drogba and Joe Cole made little impression on Liverpool's back four with Sami Hyypia and Jamie Carragher in control in the middle and Djimi Traore and Steve Finnan covering superbly on either flank.
Liverpool midfielder Dietmar Hamann taking the place of the suspended Xabi Alonso created time and space for himself and Gerrard to set up Garcia and Milan Baros in attack.
Although the Liverpool front men failed to find the net again they showed more invention than the Chelsea strikers who generally looked jaded after a long successful campaign that secured them the English League Cup in the final against Liverpool in February and the title on Saturday.