- Bojan won and scored 39th-minute penalty
- Everton injuries to Jagielka, Howard, Mirallas
- Walters not sent off for pulling back clean-through Baines
- Stoke leapfrog Everton into 11th place
Bojan Krkic's controversial penalty won a fiercely contested fixture for Stoke as Everton were left counting the cost of injuries and missed chances.
The Spaniard sprinted around James McCarthy and went down, with referee Lee Mason adjudging contact was made.
Bojan scored the spot-kick - with Everton aggrieved that Jonathan Walters wasn't sent off for dragging back Leighton Baines moments earlier.
The home side wasted openings and Phil Jagielka and Tim Howard limped off.
Injuries to Toffees captain Jagielka, goalkeeper Howard and winger Kevin Mirallas ahead of a packed festive fixture list will give Everton boss Roberto Martinez as much concern as his side's seventh defeat of the season.
Steven Naismith will miss Sunday's game at Newcastle after picking up his fifth booking of the season for a late challenge on Bojan - one of several feisty incidents at a wet and wild Goodison Park, with a total of 17 minutes stoppage time across both halves.
Stoke leapfrog Everton into 11th place with their first clean sheet in 13 Premier League matches - marshalled superbly by a bandaged Ryan Shawcross, who had half-time stitches in a head wound.
Martinez had criticised his side's "very soft" defending in their 3-0 defeat to Southampton last time out, but his changed backline - with 20-year-old John Stones brought in alongside Jagielka - only lasted 45 minutes.
Ahead of the game, Stoke boss Mark Hughes said his squad had been focusing on "getting the details right" - highlighting individual errors he felt had undermined his side's campaign.
Stoke conceded three clear first-half openings - one to Gareth Barry and two to Mirallas - but keeper Asmir Begovic was well-protected despite some late pressure.
Most of the action came in the first half, with a crunching Glenn Whelan tackle on Stones setting the early tone for a blood-and-thunder encounter.
But the game hinged on two quick-fire decisions from Mason.
At one end, left-back Baines burst through Stoke's defence and was hauled back crudely by Walters. But the official adjudged that with Baines 45 yards out and other defenders giving chase, it wasn't a definite goal-scoring opportunity.
In a pivotal 60 seconds, Bojan then latched on to a long Whelan clearance, held-off McCarthy, sped around him along the byeline and went down under what appeared to be minimal contact.
Everton manager Roberto Martinez:
"The red card isn't a debate. The moment he gives the free-kick it has to be a red, Leighton Baines is running into a central area in front of goal.
"The game completely changed in that moment.
"With the penalty, you know what striker is looking for. I don't think there's enough contact in that situation.
"It then became a really difficult afternoon for us losing two very important players in Jagielka and Howard."
Stoke City manager Mark Hughes:
"Bojan has done really, really well to get into the box and his back leg is clipped. Under those circumstances as a defender you've got to be really careful. It's a clear penalty."
"We've done the same at City and we won at Tottenham. Our away form is better than our home form. Last year maybe we didn't have the tools to be a threat on the road. Our home form will resolve itself and we'll pick up points there."
- 24HowardSubstituted forRoblesat 45'minutes
- 6JagielkaSubstituted forAlcarazat 45'minutes
- 16McCarthySubstituted forEto'oat 69'minutes
- 18BarryBooked at 78mins
- 14NaismithBooked at 28mins
- 20CameronBooked at 83mins
- 19WaltersBooked at 35mins
- 27BojanSubstituted forAdamat 67'minutesBooked at 90mins
- 10ArnautovicSubstituted forAssaidiat 76'minutes
- 18DioufSubstituted forCrouchat 90+2'minutes
- Lee Mason
- Shots on Target