Toothless Toffees struggle once again despite first half control.
A perfectly placed first half header from Kenwyne Jones sent the home side on their way before Phil Jagielka netted into his own goal to gift wrap victory in a game that the Toffees long controlled.
Both managers made changes after mixed festive periods, as Tony Pulis handed veteran utility man Danny Higginbotham a start in place of the suspended Robert Huth, while Ricardo Fuller figured upfront, replacing Jonathan Walters. For the visitors, David Moyes elected to add a striker in Louis Saha to a side that lacked a nominal forward in the draw at West Ham in midweek.
But it was the introduction of a striker for the home side that almost saw the game's first goal as a Rory Delap long throw rocketed over the heads of half the players on the pitch before being flicked on by Fuller, only for the alertness of Tim Howard to deny the Jamaican.
Saha then saw an opportunity to give the away side the lead after connecting to a corner with a diving header over Shawcross that only narrowly flew over Asmir Begovic's bar.
Stoke should have opened the scoring with the first clear cut chance of the game as a Begovic punt upfield was flicked on by Kenywne Jones and into the path of Fuller, who rounded Sylvain Distin before, with the goal at his mercy, stroking the ball casually wide from the edge of the box.
And the miss served to galvanize the visitors, who looked every inch the more composed side in the opposition half, with Tim Cahill and Mikel Arteta both showing their class as Seamus Coleman offered a threat from the right flank that saw Danny Collins go into the book for a challenge born of frustration.
But the home side were able to finally get a home goal after more than 180 minutes of fruitless huffing and puffing as Jones and Matthew Etherington linked up with the latter dribbling past Phil Neville and Coleman before delivering an inch-perfect cross for the club record signing to glance into the far corner.
Yet the score was almost level just moments later as Leighton Baines stood up an equally exquisite cross to the far corner to the loitering Cahill, who arched his header across the face of goal and only inches away the inside of the opposite post.
And goalkeeper Begovic was highly fortunate not to see red as he raced out to intercept a looping ball that Saha was chasing onto, before swiping away the Frenchman with a careless tackle that drew a yellow card from the referee's pocket.
It was the visitors who continued to threaten from that point, with Baines and Coleman both impressing by offering width and guile down either flank, with the latter feeding in a terrific ball that should have been turned in by one of a host of blue shirts, but the only real opportunity prior to the break fell to Steven Pienaar, only for the South African's effort to be deflected over by Higginbotham.
That effort summed up the travelling side's frustrations as they trundled down the tunnel having largely dominated the game but failing to turn get on to the scoresheet.
Neither manager made a change for the restart, from which Dean Whitehead went into the book within seconds for a lunge on Arteta.
And the second half continued in the vein of the first, with Everton retaining possession but failing to create much, and when a gift was presented to them as Jones headed into the path of the unmarked Pienaar, the South African could only volley spectacularly wide.
But the home side soon got into things as Everton were pegged back for long periods, with the tired Pennant replaced for Sanli Tuncay, offering more invention and pace to keep Baines detained in his own half.
As the Potters pushed forwards, Toffees boss Moyes made a double swap with 20 minutes remaining as Neville and Cahill made way for Leon Osman and Victor Anichebe.
But those changes did little to help the away side, who conceded a soft own goal moments later as a Higginbotham punt into the area was nodded on by Jones and bundled into his own net by Jagielka under pressure from Fuller.
And it should have been worse for Everton not long after as Fuller latched onto a bouncing ball but struggled to get his feet together as Howard rushed off his line to block the Jamaican one-on-one.
That flurry of activity prompted Moyes to throw on Jermaine Beckford for the dreadfully disappointing Saha, but it was the home side who continued to threaten, with Fuller and Jones both combining well to create opportunities, while Dean Whitehead saw a volley fly wide from the edge of the area.
Substitute Tuncay then came close to netting a superb left-footed half-volley after beaten Baines in the air, only for his strike to creep narrowly wide of Tim Howard's goal, while for Everton, a half-hearted flick from Anichebe struggled to test Begovic.
That chance was the last of a game that Everton fans may feel was there's for the taking, especially after a solid first half display, but Stoke supporters will relish a first home win in nearly two months, and though the second goal owed much to fortune, there was little luck in a second half in which the Potters were distinctly better than their opponents.
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