It was Liverpool's first win in five meetings this season with Chelsea, whose manager Jose Mourinho said "the best team lost". The sides drew the semi-final first leg 0-0 last week.
Central defender Jamie Carragher said Liverpool's past successes, including four European Cups, were achieved on occasions like Tuesday's 1-0 second leg victory at Anfield.
"We were desperate to get back to those days," Carragher said. "This club's been built on this type of night.
"But this was only a semi-final, the cup's there to be won. This hasn't finished yet," the England defender told ITV Sport.
"I think we were due a bit of luck (against Chelsea). There was that freak goal in the Carling (League) Cup final," Carragher said.
Newly crowned Premier League champions Chelsea beat Liverpool 1-0 twice in the league and came from behind to win the League Cup final 3-2 after extra time in February.
Liverpool captain Steven Gerrard, whose flick-on set up Luis Garcia's controversial fourth-minute winning goal, said: "We're going to final, that's the most important thing, whether it was a goal or not."
It was unclear even from television replays whether Garcia's shot went over the line before being hooked from under the crossbar by defender William Gallas.
"Credit to Chelsea, they played really well and put us under pressure. We've beaten the champions for the first time in five goes," said Gerrard, whose own goal had put Chelsea back into the League Cup final.
Mourinho said: "It was a copy of game in Cardiff where one team scored in the beginning of the game. No one knows if it was a goal, not even the linesman.
"After that, they just defended. I'm very sad we lost but you must understand what football is... I'm very proud of my players," he said after Chelsea went out of the competition at the same stage for the second season in a row.
"From my heart I hope Liverpool win (the trophy)".
Liverpool will face AC Milan or PSV Eindhoven in the final in Istanbul on May 25.
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