Despite a good start from the hosts, Stoke worked their way back into the game and went ahead just before the break after a penalty was awarded for a push in the box.
Cardiff started in fine form, with Mats Daehli pulling the strings. The Norwegian youngster found himself crowded out after a good run into the box, before finding Jordon Mutch with a through-ball, but the midfielder's effort was saved comfortably by Asmir Begovic.
Daehli was involved as Cardiff continued to look the more threatening, although it was Stoke who created the first half's best chance when a swift counter-attack allowed Stephen Ireland to pick out Peter Odemwingie, but his powerful effort was blocked by David Marshall.
Stoke improved after that and began to control the ball themselves, but they had their goalkeeper to thank for ensuring that they went in level at the break.
With a few minutes to go until half time Peter Whittingham curled a free kick up and over the wall, only for Begovic to somehow get across and tip the ball onto the woodwork and away.
Things got worse for Cardiff moments later as Arnautovic converted a penalty on the stroke of half time, after Kim Bo-Kyung was adjudged to have fouled Odemwingie in the box.