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.
Source: PA
Source: PA