Stoke were able to net their first away goal since January, but Mark Hughes will be frustrated having witnessed his team fail to close out the game, with the result taking their poor run to just one win in nine matches.
Both teams struggled to create chances during a competitive opening but in the 21st minute, Adam Smith struck the ball against the post for the home side.
The striker was making his first Premier League start for Bournemouth, but he got the last touch after Geoff Cameron had diverted the ball towards goal.
It did not take long for Bournemouth to equalise against the run of play, with Smith's work down the flank being rewarded as Stanislas provided the confident finish inside the penalty area.
However, Stoke were back in front with 17 minutes remaining as Mame Biram Diouf netted his first goal of the season from close range after Bournemouth had failed to deal with a high ball which had been sent into the box.
The home side soon went back onto the offensive with Steve Cook dragging a shot wide of the post, but they were back on level terms for a second time when Shawcross diverted Joshua King's header past his own goalkeeper.
Opportunities were few and far between during the closing stages but while Stoke will feel a great deal of frustration having failed to see out the game, Bournemouth will be delighted with a share of the spoils which sees them sit in 10th place.