Robert Huth scored the only goal of the game to give Stoke a first FA Cup victory over Wolves in the fourth-round derby clash at Molineux.
The former Chelsea defender headed home a Matthew Etherington free-kick with 10 minutes remaining.
But Wolves spurned a golden chance to earn a replay when Thomas Sorensen saved a last-minute penalty from Nenad Milijas.
Overall Tony Pulis' visiting side deserved to book a place in the last 16 after looking the more dangerous over the 90 minutes.
John Carew caused problems on his full debut after his loan move from Aston Villa, and only a series of fine saves by Marcus Hahnemann kept the visitors at bay until Huth struck.
It was Stoke's first maiden over their local rivals in the competition after six previous defeats.
Rory Delap was able to propel a series of early long throws into the Wolves box, and one of them almost led to Stoke taking the lead with the ball dropping to Carew whose shot was turned around the post by Hahnemann.
Wolves suffered an early setback when midfielder Stephen Hunt limped out of the action and was replaced by Dave Edwards.
Wolves came to life and Huth had to be alert to cut out a low cross from the byline by Matt Jarvis.
Then a mistake by Abdoulaye Faye let in Stephen Ward and his low cross-shot was parried away by Sorensen.
Carew looked hungry and shook off the challenge of Richard Stearman to leave himself with a run at goal but Hahnemann did well to block his shot.
Stoke midfielder Salif Diao became the first player to be yellow-carded when he was penalised for bringing down Milijas.
Stoke continued to look the more likely team to break the deadlock and Christophe Berra was almost caught napping by the persistence of Carew before recovering to clear.
But Steven Fletcher missed the most clearcut chance of the first half after 37 minutes.
Ward sent over a pinpoint cross from the left flank and Fletcher was perfectly placed at the far post to take advantage, but he sent his close-range header against the post.
Pulis made a half-time switch, with Diao replaced by Glenn Whelan.
Jon Walters was booked within a minute of the restart after a challenge on Milijas.
McCarthy looked upset by a challenge inside the Stoke box by Huth on Berra who went down clutching his face but referee Michael Jones waved play on.
Carew held the ball up well before releasing Etherington in space on the left but Hahnemann went down to smother his low cross.
Jarvis made a good break down the left and the cross was inviting for the onrushing Ward but his header lacked conviction and did not test Sorensen.
Hahnemann made a fine reaction save to keep out a powerful drive from Whelan after he had punched clear a long throw from Delap.
The United States goalkeeper produced an ever better save to turn a low drive from Etherington around the post.
With 10 minutes left, Huth broke the deadlock for Stoke.
Etherington swung a free-kick in from the byline and no-one picked out Huth who headed past Hahnemann.
Wolves tried to rally and Sorensen held on to a header from Sam Vokes following a deep cross by Jarvis.
Then came their big opportunity to force a replay, but Sorensen saved the penalty from Milijas after he had been brought down by Huth.