Substitute Karlan Grant's goal saw West Brom beat Championship rivals Sheffield United in the Carabao Cup to set up a second round trip to Derby.
In an entertaining first half it was the away side who came closest to opening the scoring when Rhian Brewster's shot came back off the post.
Grant headed home the winner from Callum Robinson's cross just three minutes after coming on.
Robinson and Matt Phillips then hit the crossbar in quick succession as the Baggies looked to make the win safe but ultimately one goal proved to be enough.
There was some bad news for the victors though, with striker Grant forced off with an injury before the end of the match.