But the main talking point of the game was Marouane Fellaini's clear headbutt on Ryan Shawcross, which referee Mark Halsey failed to spot.
A Shawcross own goal gifted the Merseysiders the opening goal 11 minutes before half-time, but the hosts hit back thanks to Kenwyne Jones' first top flight goal in 16 months, seven minutes after the break.
After that, both teams had chances to claim all three points, but they happily settled for a share of the spoils.
Fourth-placed Everton have now drawn nine of their last 13 Premier League away games and five of the last six, while ninth-placed Stoke stretched their unbeaten home record to 15 league games.
Everton made a lively start to the contest, with Nikica Jelavic seeing his shot from Seamus Coleman's tee-up blocked by Shawcross in the ninth minute.
The Potters fell behind in the 36th minute through an own goal from captain Shawcross, who inadvertently nodded in a Steven Pienaar cross.
Having gone in front, Everton swiftly looked to go for the jugular and Leon Osman really should have made it 2-0 but blasted wide from Leighton Baines' cut-back, drawing an angry reaction from his manager David Moyes.
Stoke appeared full of purpose after the restart and within three minutes, Tim Howard was called into action to save a mis-hit close-range volley from Charlie Adam.
However, the American was eventually beaten as Jones, retaining his starting place up front, equalised in the 52nd minute, heading Shawcross' long-range delivery past Howard.
Having broken his long scoring drought in the league, Jones looked in the mood for more and moments later he dinked the ball over Howard, only to see it hit the woodwork.
Everton then seemed lucky to escape punishment, with Fellaini appearing to headbutt Shawcross as the two players marked each other in the box. The Stoke man was left lying on the turf, but the officials took no action.
Given that the sides had drawn eight top-flight games each this season before Saturday's encounter, it perhaps came as little surprise that the points were shared.
|Stoke City||Team Statistics||Everton|
|0||1st Half Goals||1|
|5||Shots on Target||2|
|7||Shots off Target||5|
|48.5||1st Half Poss.||51.5|
|50.2||2nd Half Poss.||49.8|