Neil Warnock's men arguably edged proceedings at Selhurst Park, but a lack of cutting edge in the final third meant a below-par Stoke were seldom troubled.
Yannick Bolasie has been in tremendous form of late and the winger was once more Palace's primary attacking threat, the winger providing the assist for James McArthur to head home the opener after 11 minutes.
Stoke - who were aiming to build on last weekend's excellent 3-2 win over Arsenal - were level by the 13th minute, though, when the ball fell kindly for Peter Crouch to score from close-range.
McArthur was then denied in each half by Stoke goalkeeper Asmir Begovic as Palace failed to find a winner.
The draw leaves Palace a point above the relegation zone, while Mark Hughes' Stoke - who have still yet to record back-to-back league wins this term - climb above Everton and Aston Villa into 11th.
The hosts moved ahead from the first clear-cut opportunity of the match.
Stoke were struggling in Palace's final third and their hopes took a further blow when Bojan was replaced by Marko Arnautovic in the 55th minute - seemingly as a precaution against injury.
Begovic subsequently produced an excellent save low to his right, palming away McArthur's drilled effort from 20 yards.
The second half became something of a war of attrition with both defences on top, although Stoke did briefly threaten with a flurry of corners.
