Northern Ireland international winger Brunt struck seven minutes from time with a low left-foot drive after an excellent pass into his path by Paul Robinson.
New West Ham boss Zola, who watched the game from the stands, will officially take charge of the team on Monday and his first priority will be tightening up their defence which was alarmingly leaky at times.
The Hammers were trailing after just three minutes to a James Morrison header. Goals from Mark Noble and Lucas Neill then put the Hammers in charge only for their lead to last 60 seconds with Roman Bednar equalising from the spot.
Bednar then missed two chances to regain the initiative at the start of the second half before Brunt took advantage of more acres of space in the West Ham defence to secure Albion a hard-earned three points.
The Hammers still had a chance to grab a point in stoppage time but Scott Parker was denied by a save from Scott Carson.
Albion had gone into the game without a goal in open play in their previous three Premier League matches but they soon ended that unwanted statistic.
A left-wing cross from Brunt flashed across the face of goal and was picked up on the opposite flank by Iglesias Borja Valero whose centre was headed home from eight yards by Morrison.
It should have been the signal for Albion to take complete control. But Morrison was denied a second goal by Robert Green before the England goalkeeper had a lucky let-off in the 16th minute when he missed a corner from Jonathan Greening only for Bednar to head wide.
Robert Koren was then denied by Green when he only had the keeper to beat and Leon Barnett fired into the side-netting.
Failure to take those chances hit Albion hard as they went from leading to falling behind in the space of seven minutes.
A deep left-wing centre from Calum Davenport was headed goalwards by David Di Michele. His effort was saved by Carson but the loose ball fell invitingly to Noble who stabbed home from close range in the 29th minute.
Carson pulled off another smart save to deny Di Michele but from the resulting Noble corner Matthew Upson nodded down to Neill who pounced at the near post.
To their credit, after that double setback, Albion's response was swift and decisive. Just 60 seconds later, Barnett was sent crashing to the ground in the area by Green and Bednar scored from the spot - converting his second penalty of the season.