Everton 3 Sunderland 0
The Blues were anxious not to make a repeat of last Saturday's game against Charlton, which saw them outclassed by an inferior side and embarrassingly defeated for the first time this year.
Both teams started well, with possession evenly matched and working both keepers hard early on.
It was the visitors who had the first real chance at goal after seven minutes when Sean Thornton's early shot was caught by Richard Wright.
But the Goodison Park outfit were determined not to make it two straight defeats and responded 90 seconds later.
Leon Osman snatched the ball before crossing it to James McFadden and the Scotland international connected with a header that flew into the top right-hand corner from outside the area.
Everton continued to dominate the first half, working the Black Cats' back four and former Everton keeper Thomas Myrhe, pushing forward and creating plenty of chances inside the penalty area.
Their passing was excellent, particularly from the pint-sized Osman and midfield stalwart Lee Carsley who both ran rings around the Championship side's defence.
It was one of Carsley's inspired passes that £6million transfer window signing James Beattie his first goal for the Blues.
His 27th minute cross was met at the feet of the former Southampton striker who fired home the 20-yard shot.
Norwegian international Myrhe could well have saved the shot but the unfortunate Danny Collins helped it on its way.
From then it was all over for Sunderland. Everton are 20 places above them in the league and proved exactly why they thoroughly deserved fourth place in the Premiership.
The home side had another two opportunities to pull further ahead but only some plucky saves from their former keeper kept the score at 2-0.
The visitors' misery continued into the second half as Everton maintained their stranglehold over the game.
Two early chances from Thornton were caught by Wright and by the 80th minute it was all over.
An Osman cross found Australian midfielder Tim Cahill who slipped the ball into the net to guarantee David Moyes' men a place in the fifth round of the FA Cup.
MAN OF THE MATCH: James McFadden (Everton) Scored the first and was a constant thorn in the side of the Sunderland defenders with his intelligent movement.