Stoke had the lion's share of early possession and put the London club on the back foot around 20 minutes with youngster Frazer Richardson and John Eustace both going close but failing to capitalise.
However, after being suppressed by City pressure for a period of time, Palace gained an unexpected advantage when Tony Popovic searched out Andy Johnson from the right and he spectacularly headed the ball into Ed de Goey's top left corner from 15 yards.
Johnson could have added another three minutes before half time when Dougie Freedman presented him the ball six yards in front of goal, but de Goey stood strong and saved well down low.
The Potters were hungry after the break but the loss of Gifton Noel-Williams to injury didn't help their cause.
Richardson popped up again in the 60th minute and came close to nicking the equaliser, but his powerful drive took a slight deflection past Thomas Myhre's post.
Palace's counter attacks had worked once before and nearly worked again when Tommy Black played Johnson through on goal, and he managed to round Wayne Thomas but was denied again by a point-blank de Goey save.
Stoke's final push to salvage a point came to no avail with Myhre rescuing Palace on a couple of occasions with magnificent saves.