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.
Everton have not won at Anfield since 1999 and, in truth, they never looked like getting anything from their latest visit.
The Reds looked more organised from the outset, attacked with pace and in numbers, and only a couple of good saves from Joel Robles prevented the hosts from taking the lead much earlier than the 43rd minute.
The sending-off of Funes Moris, after he stood on Origi’s ankle, arguably ended any hopes of an Everton fight-back but there had been little to suggest that was ever on the cards.
Man of the match – James Milner