Two early strikes from Jo and Joleon Lescott had the Blues cruising and looking like notching up a cricket score having had no efforts to save from Tony Pulis' men.
But a Ryan Shawcross goal just after the break brought a nervy second 45 for the Blues, who managed to bag a third in added time to produce a scoreline that slightly flattered their performance.
The home started the brighter with Steven Pienaar and Leighton Baines allowed to repeatedly charge down the left and the pair linked up well to carve open the Stoke defence inside the first five minutes, but a well-timed tackle from Andy Wilkinson averted the danger.
The Blues continued with the pressure and a minute later Baines quickfooted his way to the byline and found Leon Osman, but a similar tackle from Danny Higginbotham was enough to keep the scores level.
Despite former Everton striker James Beattie being in the form of his life, it was David Moyes' men who looked the most threatening and with only 17 minutes gone they deservedly found the opener.
A long punt upfield was easily won by Jo to play in Marouane Fellaini, who with his first touch sent it back to the Brazilian, who strode into the box and drilled it low beneath Thomas Sorensen.
Having won every high ball hoisted forward, partners Beattie and Mamady Sidibe couldn't manage to latch on to any second balls and never troubled the organised Everton defence.
The home side were making all the running pinning Stoke deep inside their own half and making his 100th appearance for Everton, Lescott marked his milestone with his side's second goal.
Under no pressure to hurry the ball Osman was allowed to control and pick his cross from the edge of the area and Tim Cahill rose to sting the palms of Sorensen with a strong header.
While still picking himself off the deck the keeper could do nothing to stop Lescott steaming in at the back post for the easy tap-in.
Unlucky not to have found a third minutes before the break, Everton were spreading the ball about like a training exercise when Jo found himself running at the red and white backline and a neat ball to the feet of Osman brought a clever turn and a curling effort which flew inches wide.
Having failed to get a single shot on target in the first half, Stoke looked to be in for a rout with the introduction of Louis Saha for the Toffees, but they forced their way back into the game on 52 minutes through Shawcross.
An inswinging corner from Liam Lawrence was not attacked by a Blue shirt and Shawcross rose head and shoulders above all surrounding and powered his header past a scrambling Tim Howard.
Replenished by the goal Stoke were throwing bodies forward and it was Shawcross again who could have brought the scores level minutes later, after another corner wasn't cleared and Higginbotham's header bounced inches from his outstretched boot.
The introduction of Ricardo Fuller only troubled the Blue defence even further and after winning a knock down to Salif Diao, his blast was blocked by a last second lunge from Lescott.
Everton still looked a threat on the break and Phil Jagielka whipped a ball into the near post, but the keeper missed his punch fooling Saha, who was closing in behind him.
Sorensen kept his side in the game on 73 minutes with a double save from Jo, once at the feet of the goalscorer and then his attempted curling rebound, much to the appreciation of his team-mates.
With only four minutes on the clock Everton broke after substitute Jack Rodwell won the ball and through Fellaini, Osman was released and surged forward before drilling it at Sorensen.
But after dangerously spilling the ball at the feet of Saha, the keeper recovered to save the Frenchman's rebound with his body.
The game was put out of Stoke's reach in added time when Baines launched a high ball to Fellaini, who took the ball down from over his shoulder with his right and slotted home with his left in what was the move of the game.