The hosting Baggies broke the deadlock with their first meaningful attack of the match. Billy Jones found Chris Brunt with a cross from the left and the Northern Ireland international sent his first-time effort into the roof of the net after eight minutes.
In response, Mick McCarthy's Wolves forced Ben Foster into a diving save when winger Adam Hammill struck from distance.
Despite edging the possession statistics for large parts of the match, the visitors were unable to force an equaliser and their failure to do so was punished 15 minutes from time.
Wolves refused to give up the match, with Adlene Guedioura going closest after producing an acrobatic volley.
However, they were unable to find a route back into the match, allowing West Brom to move out of the relegation zone with the three points.