A slow and scrappy start struggled to produce any chances until a well-worked passing move in the 48th minute by Palace ended with Dougie Freedman playing a throughball to Shaun Derry whose 15-yard shot was saved by Neil Cutler.
Freedman could have scored himself in the 30th minute when his mazy dribble in the Stoke box took him past two defenders but Cutler's block helped James O'Connor to clear.
Stoke managed to get nearer the goal towards the end of the first half starting in the 39th minute when Bjarni Gudjonsson's second 20-yard free-kick curled just over Nik Michopoulos' left angle.
The Potters went close again on the stroke of half time when Peter Hoekstra passed Andy Cooke in a crowded box but his close-range shot flew inches over the bar.
Both teams seemed to up their tempo after the break.
A quick break for Palace saw Freedman link with Dele Adebola who out-sprinted Peter Handyside to power a left-footed drive past Cutler from 10 yards in the 77th minute.
Steve Cotterill's side then stepped on the gas in the 85th minute when a ball from the byline by Wayne Thomas found Marc Goodfellow who played it inside for super sub Chris Iwelumo to neatly finish from 10 yards to the left of Michopoulos.
Stoke City boss Cotterill was fairly pleased with his team's performance saying: "I've got no complaints about how we competed for the whole 90 minutes, but we could have passed the ball better and created more chances."