Ousmane Dembele's two second-half goals sealed a 4-0 aggregate victory on Tuesday (Wednesday AEST) and kept PSG on course to defend European club soccer's biggest prize.
Dembele's first goal killed off Liverpool's fight as the Premier League club went in search of another famous Champions League comeback. The Ballon d'Or swept a low left-footed shot from the edge of the area past goalkeeper Giorgi Mamardashvili to quieten the home crowd and ease PSG tension.
His second came at the end of a sweeping move in added time.
Dembele had been guilty of wasting chances in the first leg to effectively put the tie to bed and he failed to take two more first-half opportunities to put the French champion further ahead on Merseyside.
But his winner was dispatched with precision - nestling in the bottom corner.
PSG will play either Bayern Munich or Real Madrid in the semis.
Atletico Madrid are also through to the last four, for the first time in nearly a decade, holding on after an early charge by Barcelona.
Atletico advanced 3-2 on aggregate despite a 2-1 loss to the Catalan club in the Spanish capital.
Barcelona scored twice in the first 24 minutes to level the tie through Lamine Yamal and Ferran Torres.
Atletico struck back with a goal by Ademola Lookman, but the hosts played a man down from the 79th after defender Eric GarcÃa was shown a red card for fouling Alexander Sorloth to stop a breakaway.
Diego Simeone's side will face Arsenal or Sporting Lisbon next.
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