The first half finished goalless but Birmingham came within a whisker of opening the scoring three minutes before the break.
Birmingham would come to rue the miss because, on the hour mark, Grealish played a pass into the path of Adomah, who shifted the ball onto his right foot and rifled home from 18 yards.
Villa went on to seal the win nine minutes from time when Conor Hourihane pounced on a poor clearance to slam a ferocious strike up over Stockdale and into the net from 20 yards.
The Blues went on to end the game with 10 men after Cheikh Ndoye was shown his second yellow card after an altercation with Terry in the Villa box.
ASTON VILLA (4-1-4-1): Johnstone; Elmohamady, Terry, Chester, Hutton; Jedinak; Snodgrass, Hourihane, Adomah (Whelan 89'), Grealish (Bjarnason 84'); Hogan (Grabban 79')
BIRMINGHAM CITY (4-2-3-1): Stockdale; Jenkinson, Roberts, Dean, Colin; Kieftenbeld, Ndoye; Maghoma (Jota 76'), Davis (Adams 82'), Boga; Gallagher