After a goalless first leg, the second meeting at Anfield was settled in controversial fashion with Garcia scoring just five minutes in.
Steven Gerrard flicked on John Arne Riise's pass into the path of Milan Baros, who knocked it over the out-rushing Petr Cech but went down under the challenge of his fellow Czech Republic international team-mate.
The ball fell for Garcia to apply the finishing touch as William Gallas scrambled to block his shot.
Chelsea appealed that the ball never crossed the line and replays proved inconclusive, but the goal was given and Liverpool were bound for Istanbul, much to the disgust of Chelsea manager Jose Mourinho.
"The best team lost," the Portuguese said after the match.
"The linesman thought they scored one goal and we didn't score, so we lost.
"I don't want to criticise them but they played the way they want; they fought and fought and fought. Of course we are disappointed, but I am very proud of my players."
Whether or not there was a slice of fortune in it for Liverpool, they made the most of their opportunity.
Three weeks later, in one of the most dramatic Champions League finals, Rafa Benitez's side recovered from 3-0 down to beat AC Milan in a penalty shoot-out, lifting the European Cup for the fifth time in the club's history.