The Premiership Reserve League (North) game was switched to Billingham Synthonia's Central Avenue ground after flood damage at the Riverside on Sunday.
After a goalless first half Boro stormed into a 2-0 lead thanks to two goals from Jamie Cade, West Brom replied with a goal in stoppage time from Simon Brown.
Boro boss Mark Proctor will be delighted to win his first game in charge following his 'promotion' from the youth set-up last season.
Boro team:
Russell
Stockdale
Taylor
Gulliver
Davies
Smith (Close)
Wilson
Johnston
Cade
Morrison (Dove)
Downing