John Arne Riise's last-minute own goal gave Chelsea a 1-1 draw at Anfield.
Goals from Didier Drogba and Fernando Torres took the second leg to extra time.
Frank Lampard had returned for the match only days after the death of his mother and scored a crucial penalty, prompting an emotional celebration.
Drogba struck a second and although Ryan Babel pulled a goal back for Liverpool, Chelsea reached their first Champions League final, as manager Avram Grant marked Holocaust Remembrance Day.
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