Goals from Gerard Deulofeu, Seamus Coleman, Bryan Oviedo and Romelu Lukaku earned Everton their biggest win of the season to maintain their unbeaten record in 2013 at home.
The scoreline could have been even bigger had it not been for Asmir Begovic as Everton dominated from the first whistle against a disappointing Stoke side.
Everton started brightly and they created their first chance of the game after just two minutes when Deulofeu saw his low free-kick from the edge of the box tipped round the post by Begovic.
The home side continued to call the tune in the early exchanges and on 15 minutes the lively Deulofeu fashioned an opening for himself with some neat footwork inside the box and fired in a shot which was punched away by Begovic.
Two minutes later James McCarthy was inches away from breaking the deadlock when he played a neat one-two with Lukaku and curled his left-footed shot just the wrong side of the post.
Begovic came to Stoke's rescue on 26 minutes when he produced a brilliant save to keep out Leon Osman's deflected effort, changing direction in mid-air to palm away the ball.
Stoke created their first chance of the game two minutes before the break when Peter Crouch headed the ball down to Jon Walters on the edge of the box only for his strike partner to hit his shot straight at Tim Howard.
Everton made the breakthrough their dominance deserved on the stroke of half-time with a wonderful effort from the impressive Deulofeu.
Deulofeu played a one-two with Steven Pienaar to burst into the box and then exchanged passes with Gareth Barry before smashing his shot past Begovic at his near post.
Everton doubled their four minutes after the break with a somewhat fortunate goal from Coleman.
Deulofeu was again at the heart of it as he ran down the left and picked out Barry inside the box and his touch fell into the path of Coleman who sliced his left-footed shot past a stranded Begovic.
Stoke were struggling to contain Barcelona loanee Deulofeu and the Spaniard was denied his second goal on 54 minutes when he raced clear from a long throw from Howard to go one-on-one with Begovic, but the big keeper did well to keep out his shot with his legs.
Everton put the game beyond Stoke on 58 minutes with Oviedo scoring his first goal for the club as he picked up a corner on the edge of the box and burst past a challenge from Charlie Adam before drilling a right-footed shot into the bottom corner past Begovic.
Stoke created their best chance of the game five minutes later when substitute Kenwyne Jones played Crouch in on goal, but Howard stood up well to block the former Liverpool man's shot.
Everton grabbed a fourth goal on 79 minutes with Oviedo getting down the left and picking out Lukaku to convert the simplest of chances from just four yards out to continue his rich vein of form.
Everton substitute Nikica Jelavic really should have made it 5-0 in the final minute when fellow substitute Kevin Mirallas played him in on goal, but Begovic kept out the striker's shot with his legs.