Niall Ennis put the visitors in front on 51 minutes before Benny Ashley-Seal (pictured) made it 2-0 with a 70th-minute penalty.
Callum Morton pulled a goal back for the Baggies, also with a penalty, but Wolves held on.
They moved up to eighth with three matches remaining and are three points adrift of Middlesbrough, who occupy the final play-off position. West Brom remain bottom.
See: West Brom report
West Brom: 9 Apr v Brighton (A) PL2
Wolves: 9 Apr v Leicester (A) PL Cup