The Potters fell behind in the 36th minute through an own goal from captain Ryan Shawcross, who inadvertently nodded in a Steven Pienaar cross.
Jones, retaining his starting place up front with Peter Crouch again named as a substitute, equalised in the 52nd minute, heading Shawcross’ long-range delivery past Tim Howard.
The previous time Jones – who also hit the post – had netted in the top flight was in August 2011.
A draw was probably a fair result for both ninth-placed Stoke and fourth-spotted Everton, although the visitors might have had Marouane Fellaini sent off if the match officials had spotted the midfielder’s apparent headbutt on Shawcross in the second half.
And, given that the sides had drawn eight top-flight games each this season before today’s encounter, it perhaps came as little surprise that the points were shared.
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.
Two minutes later the visitors appealed for a penalty when Pienaar’s strike appeared to hit Glenn Whelan’s arm, but referee Mark Halsey waved for play to go on.
The Potters could only respond with tame efforts from outside the box by Matthew Etherington and Jones.
Just after the half-hour mark, though, they passed up a clear opportunity when Whelan swung in a corner, Jon Walters headed the ball back and an unmarked Steven Nzonzi could only nod it into the arms of Howard.
Soon after Shawcross was on hand to hook Steven Naismith’s goal-bound attempt away from danger, before Howard – making his 200th consecutive league appearance – dived to keep out a curling Etherington shot.
Stoke’s defensive record has been formidable and they had only let in two goals at home in the league this term going into this game.
It was, therefore, somewhat fitting that, when Everton managed to make a breakthrough, it was not a Toffees player who scored.
Instead, the ball went over Asmir Begovic and in having come off the head of the unfortunate Shawcross, who had been trying to clear Pienaar’s 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, Howard was called into action to save a mis-hit close-range volley from Charlie Adam.
Another four minutes passed before the American was beaten as Jones headed home from Shawcross’ long ball into the box.
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.
Potters boss Tony Pulis shuffled his attack by introducing Cameron Jerome for Adam and Crouch for Jones, and the two new men were soon in the thick of the action.
With 12 minutes of normal time remaining, Jerome found himself through on goal and saw his shot come off the legs of Howard, with Crouch’s follow-up lob then being headed away by Sylvain Distin.
Another Potters substitute, Michael Kightly, struck off-target in the closing stages, as did Pienaar at the other end.