The Potters' first-half dominance was reflected in centre-back Robert Huth's eighth goal of the season, but Frederic Piquionne's clear handball was missed by referee Mike Jones as the striker went on to score.
When former Hammer Matt Etherington missed a penalty seconds into the second half it seemed it was not to be Stoke's day but Danny Higginbotham drilled a free-kick through the wall which goalkeeper Robert Green could only push onto a post and into the net.
Stoke took the lead in the 12th minute when Huth planted a straightforward header past Robert Green following Rory Delap's long throw into the six-yard area.
The visitors were literally handed a route back into the game on the half-hour when Thomas Hitzlsperger's ball over the top saw Piquionne get beyond Huth, but the striker blatantly used his upper arm to control the pass before lobbing it over Thomas Sorensen.
Etherington's penalty - after he had been fouled by Scott Parker - was saved by Green, but Stoke continued to look more threatening and Higginbotham smashed home a low shot which was so powerful Green could only palm it on to the post and back into the net and after Matthew Upson crashed a header against the crossbar with four minutes to go Stoke hung on for only the fourth FA Cup semi-final in their history.
Source: PA
Source: PA