Divock Origi and Mamadou Sakho headed in two goals in as many minutes at the end of the first half.
Everton lost Ramiro Funes Mori for a nasty challenge on Origi, who had to be replaced by Daniel Sturridge.
The substitute then drove in a third before Philippe Coutinho's curled finish completed an emphatic win.
The result keeps Liverpool in with an outside chance of a top-four finish. They are seventh on 54 points, six points behind Arsenal in fourth while Everton are 11th on 41 points.