The Republic of Ireland international returned from a long-term knee injury with a second-half double to lift Damien Johnson's side to seventh place in Division 2.
Stokes opened the scoring on 57 minutes with a curling strike before diverting a Daniel Butterworth effort into the back of the net just after the hour mark.
The visitors reduced the deficit with a consolation strike three minutes from time through Callum Morton, but remain in ninth place as a result of the defeat.
Blackburn next host Fulham at Leyland County Ground on 18 April, while West Brom take on Stoke City at the bet365 Stadium the previous day.
See: West Brom report