Michael Keane pulled out back for the Toffees, only for Origi to score his second shortly after.
Sadio Mane made it 4-1, after he had set up Origi's two goals, before Richarlison scored on the stroke of half-time.
Gini Wijnaldum scored on the 90th minute mark to round out what was a dominant victory for the Reds, who have restored their eight point lead at the top of the table.
Speaking after the game, manager Jurgen Klopp said: "All the goals were incredible, outstanding. Wonderful goals, sensational passes, super pieces of football. I loved it a lot.
"We needed fresh legs and I had to show my respect to the boys in the squad, that's all. They proved it. It is much more fun making changes, all of the boys are ready to deliver performances like this.
"It was a massive moment in my first season when Divock Origi got injured in the derby. It changed his career for a bit."