Dunn headed home a Bradley Orr cross to grab the point Rovers' second half performance deserved, and frustrate a Villa side denied the chance to move further clear of the drop zone.
Charles N'Zogbia had rocketed Alex McLeish's men into a 24th minute lead and such was their dominance it seemed likely Villa would go on to claim a comfortable win.
But Rovers responded in superb fashion with Junior Hoilett, Scott Dann and Morten Gamst Pedersen all coming agonisingly close before Dunn's header secured their vital point.
Villa dominated the early quarter of an hour, pinning the hosts back in their own half and almost grabbing a fourth minute lead through Marc Albrighton.
N'Zogbia picked up the ball deep the Rovers box and laid the ball back to the midfielder, who lashed his shot over the bar from eight yards.
Pedersen headed away a dangerous corner from Albrighton before Rovers had their first chance when Pedersen's goalbound drive was blocked by the head of Stephen Warnock.
Villa grabbed a deserved lead in the 24th minute when Carlos Cuellar threaded the ball to N'Zogbia in the box and he slammed a left-foot shot past Paul Robinson into the roof of the net.
N'Zogbia almost grabbed his second in the 44th minute when N'Zogbia struck a low, close-range shot which was superbly tipped away by Robinson.
And for all Villa's dominance, Steve Kean's men almost grabbed an equaliser with the last kick of the first half when Junior Hoilett met a Pedersen cross but shot over from six yards.
Rovers looked brighter after the restart and came close to an equaliser in the 46th minute when Martin Olsson's low cross from the left just eluded Ayegbeni Yakubu in front of goal.
Villa responded with a swift move which ended with Robinson blocking a low shot from Stephen Ireland, then recovering well to smother an attempted follow-up from Alan Hutton.
The home side had another chance in the 55th minute when Steven Nzonzi headed across the box and Dann jumped to direct another header onto the roof of the net.
Rovers were enjoying their best spell of the game and came close again in the 61st minute when substitute Dunn fed Hoilett, whose drive was parried by Shay Given.
Given denied Rovers again in the 70th minute by reacted superbly to block a Pedersen shot after Orr's initial ball into the box had only been half-cleared.
Villa came close to extending their lead in the 79th minute when Robinson got down well to palm away Gabriel Agbonlahor's header from a Warnock cross.
But Rovers grabbed the equaliser their second half performance deserved in the 84th minute when Orr floated in a ball from the right and substitute Dunn headed past Given at point-blank range.
Villa substitute Barry Bannan immediately responded with a long-range drive which Robinson did well to tip round his left-hand post.