كتب : وكالات
Simao Sabrosa stunned the home crowd in the 36th minute when he scored against the run of the play while Fabrizio Miccoli sealed the victory in the closing stages.
The result capped a miserable tie for Rafael Benitez's side who lost 1-0 in the first leg's dying seconds and lift Benfica to their first last-eight appearance since 1995.
Liverpool international striker Peter Crouch almost broke the deadlock early in the first-half when his header sailed past the goalkeeper but hit the woodwork.
Benfica captain Simao shocked Liverpool when he curled a long-range shot that beat keeper Jose Reina.
Miccoli put the last pin in Liverpool's coffin in the dying seconds when he controlled a powerful cross and hammered an acrobatic side-kick into the back of the net.