Tim Howard made his 200th consecutive appearance in the EPL but saw the Potters come from behind as Fellaini headbutted a player and Jones equalized.
Stoke extended its unbeaten home record this season with a hard fought 1-1 draw with the high-flying Toffees.
The hosts went behind in the first half but showed great resolve to level things up early in the second half to claim a point. Both sides wasted late chances but in truth a draw was very much a fair result.
An own goal from Ryan Shawcross broke the deadlock just before halftime, the defender flicking a Steven Pienaar cross beyond Asmir Begovic in the Stoke goal to give the visitors the lead. The Potters were level seven minutes into the second half as Kenwyne Jones rose to meet a Shawcross ball and head beyond Tim Howard in the Everton goal.
Stoke welcomed back Charlie Adam after his one game suspension with the Scot replacing Dean Whitehead in the center of midfield, and boss Tony Pulis opted for Andy Wilkinson to fill in at the back for the suspended Ryan Shotton. A hamstring injury to Kevin Miralles meant that Everton boss David Moyes had to make one change to the side that beat Tottenham, Steven Naismith the man chosen to fill the Belgian’s boots.
In a competitive first half both sides had half chances to open the scoring but they lacked the accuracy to test either keeper. Darron Gibson and Seamus Coleman created a great chance for Nikica Jelavic in the tenth minute but his low shot from inside the penalty was well blocked by Ryan Shawcross.
The deadlock was broken in the 36th minute with a wonderful header from a Shawcross but unfortunately for the Stoke skipper it was into his own goal. Neat build up play from the visitors down the left created a chance for Steven Pienaar to cross and as Shawcross attempted to clear the cross his flicked header flew over Asmir Begovic's dive and into the top corner.
Seven minutes into the second half the hosts were level after a great header from Jones punished bad play from both Jagielka and Howard. Shawcross delivered a lovely ball from the half way line for Jones to attack, he rose above Jagielka and headed towards goal. It appeared Howard would easily save it but he got his bearings all wrong and allowed the ball to squeeze between himself and the post.
The game then had its most controversial moment as a Marouane Fellaini headbutt on Shawcross went unpunished by referee Mark Halsey. The two men were jostling for position inside the Stoke box waiting for an Everton corner when the Belgian turned and headbutted the Stoke captain but he escaped any punishment.
The introduction of Cameron Jerome and Peter Crouch gave Stoke more impetus in the closing moments of the game but Howard did well to save from both men from dangerous situations.