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Villa, who remain unbeaten after five draws and one win from their opening six matches, looked set for fifth place in the table as they led through a controversial second-half penalty from Scotland midfielder Barry Bannan.
Referee Michael Oliver ruled Armand Traore, who joined QPR from Arsenal last month, pulled Gabriel Agbonlahor's shirt in the 58th minute, though TV replays appeared to show the defender made minimal contact if any and no Villa player appealed for an infringement.
Traore's misery was completed after 90 minutes when he was sent off for a second bookable offence for a late lunge on Villa's Marc Albrighton.
That seemed to set the seal for Villa's victory but a minute later a QPR break ended with Villa defender Stephen Warnock deflecting Heidar Helguson's cross on to Dunne's knees and he could not stop the ball crossing his own line for his ninth Premier League own goal.
The result left Villa in eighth place and QPR ninth. The weekend programme will be completed on Monday when Norwich City host Sunderland.
Manchester United top the table on goal difference from Manchester City.