The home side dominated for much of the game, but failed to create chances, and were punished by an instinctive finish from the German defender, following some sloppy defending
In a relatively scrappy affair, Robert Huth’s 15th minute effort was enough to secure all three points for the Potters.
The home side pushed for an equaliser for much of the game, but never really came close to threatening the Stoke goal.
David Moyes rewarded Apostolos Vellios with his second start for the club, following his goal at Bolton last weekend, with Louis Saha dropping to the bench.
Meanwhile, Phil Neville, Sylvain Distin and Jack Rodwell all returned to the bench for the Toffees after overcoming injuries.
For the Potters, Tony Pulis made wholesale changes following his side’s Europa League exploits midweek.
Just Ryan Shotton and Huth survived the 1-1 draw with Dynamo Kiev, with Peter Crouch and Jonathan Walters leading the line.
Everton had started brightly but failed to make their dominance pay, and they were punished just fifteen minutes in.
Following a cleared Stoke corner, the ball fell nicely for Dean Whitehead on the edge of the Everton penalty area.
The midfielder composed himself before volleying a low effort at goal, only for Huth to divert the direction of the ball and prod his side into an early lead, with Tim Howard laid helplessly on the floor.
The goal did little to alter the pattern of the game, with Moyes’ side continuing to dominate possession, but the Stoke back line held firm to see them head into the half time break with a 1-0 lead.
Everton began the second half in a similar fashion to the first, dominating possession and flooding men forward, but still the Stoke defence remained firm.
Any Stoke threat predictably came via set pieces, with the height of Crouch proving a constant source of danger.
Referee Lee Mason had been the villain of the piece for the Goodison faithful, and he was again the focus of their frustration midway through the second half.
Following hesitation from Huth, Tim Cahill found himself bearing down on goal. Thomas Sorensen came to meet the Australian, only to miss the ball and wipe him out on the edge of the area.
Mason waved away Everton appeals, to the increasing frustration of the home crowd.
The Goodison Park outfit continued to press for an equalising goal, as Moyes had one last roll of the Everton dice, replacing the ineffective Vellios with Denis Stracqualursi.
Johnny Heitinga had a great chance late on to snatch a point, but he couldn’t quite reach Leighton Baines’ superb cross.
The defeat was Everton’s fourth home loss of the season, one more than they managed during the whole of last season.
Tony Pulis’ men move up to eighth in the table following the victory, with Everton a further two places behind in 10th.