Origi had put the Reds ahead two minutes before the break and defender Mamadou Sakho doubled the advantage two minutes later.
Everton faced a huge task to get back into the game.
And Funes Mori made things even worse with a reckless tackle on Liverpool’s goalscorer.
Daniel Sturridge replaced Origi and made the visitors pay by bagging the Kop’s third of the night on 61 minutes.
Philippe Coutinho made it 4-0 15 minutes from the end to round off a miserable night for the Toffees.