The hosts were in complete control throughout the match and were rarely troubled by their Championship opponents.
Ross Barkley opened the scoring on 35 minutes, slotting home on the left after clever work from Bryan Oviedo.
The lead was then doubled just before the break as Nikica Jelavic latched onto a mistake from Karl Henry and smashed the ball past Julio Cesar.
Jelavic grabbed a second on 68 minutes, guiding home Oviedo's cross, and missed the chance of a hat-trick moments later as his penalty hit the bar.
Seamus Coleman rounded off the scoring with a side-footed effort from 20 yards for his sixth goal of the season.
Here's a look at some Everton-related talking points to emerge from this contest.