Oussama Assaidi’s fourth goal of the season gave Stoke the lead before Leighton Baines' last minute penalty rescued a point for the Toffees.
Mark Hughes welcomed back Marc Wilson and Glenn Whelan from suspension in place of Wilson Palacios and Andy Wilkinson, whilst Roberto Martinez welcomed back goalkeeper Tim Howard.
Everton went into the game in the top four after their 2-1 win over Southampton, whilst Stoke languished in 12th with back to back losses after conceding eight goals in their last two games.
Stoke’s first real chance fell to an inform Assaidi, after Jon Walters crossed the ball from the right Charlie Adam missed it and the Moroccan fired a shot straight at Howard.
Kevin Mirallas responded with a superb strike which beat everyone except the Stoke crossbar before the Belgian fired his free kick at Thomas Sorenson’s post.
The Potters brought on Jack Butland for his Premier League debut in a second-half change for the injured Sorenson.
Assaidi found the breakthrough early in the second half when the ball dropped to the on-loan Liverpool midfielder outside the area and he sliced his shot from 22 yards low past Howard for his third goal in six games.
The Toffees tried to respond through Baines, but skipper Ryan Shawcross headed clear.
The England defender then crossed for Mirallas and the Belgian stuck the ball towards goal from 12 yards but Eric Pieters made a fantastic block to keep the Potters in front.
Peter Crouch and Assaidi combined in the closing stages to try and double Stoke's lead but they were cut out by good defending.
Jermaine Pennant then fouled Leon Osman and referee Andre Marriener pointed to the spot. Baines stepped up and sent Butland the wrong way in injury-time to seal a point, but Everton still drop out of the top four.
Write for GiveMeSport! Sign-up to the GMS Writing Academy here: http://gms.to/1a2u3KU