After a lacklustre first-half, Everton stepped up a gear after the break and put Sunderland to the sword.
Magaye Gueye broke the deadlock when he pounced on a loose ball in the box and lashed a shot past Simon Mignolet.
Two quick-fire wonder goals from Steven Pienaar and Leon Osman put the result beyond doubt, before Victor Anichebe added a fourth.
With the Toffees preparing for Saturday's crunch game at Wembley, David Moyes rested Leighton Baines, Tim Cahill and Nikica Jelavic.
In the absence of their star men, Everton struggled to create in the final third of the pitch. A subdued Goodison Park had to wait half an hour for the first goalmouth action.
Gueye attacked from the left wing and pulled the ball back for Pienaar, but the South African international could only send the ball over the bar.
The home side continued to dominate, but almost found themselves a goal behind when Stephane Sessegnon came within a whisker of scoring a goal of the season contender.
The Benin striker sent an acrobatic overhead kick just past the right hand top corner after connecting with a Sebastian Larsson cross.
It wasn't until the 40th minute that a goalkeeper was tested. James McFadden worked space for a shot from 20 yards that his low, curling effort was comfortably saved by Mignolet.
Sunderland's number one wasn't afforded such mercy after the interval. The hosts made a bright start to the second half and took the lead in the 52nd minute. Mignolet was unable to hold on to a rasping shot from Osman and Gueye seized upon the rebound to smash the ball into the back of the net.
The goal put Moyes's side in complete control and two of their star performers on the day, Osman and Pienaar, got the goals their all action displays deserved.
Pienaar was the first to strike. The on-loan Tottenham midfielder received a pass just inside the box and bent a perfectly measured shot into the far corner beyond the reach of an outstretched Mignolet.
There was little respite for the Belgium goalkeeper, who was picking the ball out of the net minutes later when Osman produced a carbon copy of Pienaar's goal.
Substitute Anichebe made it three goals in five minutes when he spun in the box and volleyed the ball past Mignolet, via Jack Colback's chest.