The Potters nudged ahead after a long period of pressure in the 16th minute when a long corner by Bjarni Gudjonsson found Wayne Thomas at the back post, who knocked it back in for the towering Chris Iwelumo to head home off the underside of the bar.
Sheffield Wednesday equalised against the run of play in the 23rd minute when Allan Johnston squeezed across from the left which flew across the face of goal and met by the on rushing Gerald Sibon, who slid in to convert inside Steve Banks left post.
Going into half time, the match was anything but boring with end to end action and no shortage of chances.
The potters took the lead again in the 66th minute when a looping cross from Peter Hoekstra on the left found Chris Greenacre, whose header was palmed on to the post to leave Brynjar Gunnarsson to try his luck, but it was Chris Iwelumo who finally headed home.
Wednesday wouldn't be beaten and in the 72nd minute a pass at the edge of the area found Adam Proudlock, who unleashed a superb left-footed shot that rocketed into BanksÂ’ top right corner, leaving the Stoke supporters stunned.
Stoke left it until the 90th minute to clinch the win, when a long ball forward by Marcus Hall was headed on by Iwelumo and dummied by Greenacre to allow Gunnarsson to fire under Chris Stringer to make it 3-2.
Owls manager Chris Turner said: "I'm disappointed that we didn't hang on to the draw at the end of the day.
"I don't think we coped well. We're battling away but sometimes it feels like it's against all odds."