The Saddlers held onto their slendour lead until the break but four minutes into the second period Villa drew level. Darius Vassell volleying home from 12 yards.
Eight minutes later Saddlers substitute Gary Birch scored what proved to be the winner - firing in a shot from out wide that Postma really should have dealt with.
ASTON VILLA: Postma, Delaney, Samuel, Mellberg, Alpay, McCann, Barry (Hadji, 73mins), Hendrie, Hitzlsperger (Davis, 75mins), Vassell, Allback (Dublin, 65mins).