Dunn converted a Bradley Orr cross five minutes from full-time to keep Steve Kean's strugglers within touching distance of climbing out of the Premier League relegation zone.
Rovers, who fell behind to Charles N'Zogbia's first half strike, remain third bottom, but they are behind Wolves and QPR only on goal difference.
Alex McLeish's Villa stay eight points clear of the bottom three, but this was another frustrating result for the under-fire boss.
Villa almost grabbed a fourth minute lead through Marc Albrighton. N'Zogbia picked up the ball deep the Rovers box and laid the ball back to Albrighton, who lashed his shot over the bar from eight yards.
The visitors kept up the pressure and took the 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.
N'Zogbia almost grabbed his second in the 44th minute as his close-range shot was superbly tipped away by Robinson.
For all Villa's dominance, Kean's men almost grabbed an equaliser with the last kick of the first half when Junior Hoilett met a Morten Gamst Pedersen cross but shot over from six yards.
Robinson had to block a low shot from Stephen Ireland and then smothered an attempted follow-up from Alan Hutton as Villa made a lively start to the second half.
Villa goalkeeper Shay Given denied Rovers in the 70th minute by reacting 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.
But Rovers grabbed the equaliser their second half performance deserved in the 85th minute when Orr floated in a ball from the right and Dunn headed past Given from close-range.
Source: AFP
Source: AFP