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.
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.
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 Marouane 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.