Blues defender Roger Johnson put Alex McLeish's side in front early in the second period.
Craig Gardner failed to make full contact on his low drive but David Murphy flicked the ball on and Johnson applied the finishing touch.
But Collins made no mistake from close range to salvage a share of the spoils for Villa.
Villa dominated the opening phase and final part of the game and hit the woodwork on three occasions, but Birmingham also squandered several clear-cut opportunities.
Source: PA
Source: PA