Jason Shackell's 32nd-minute strike has put Burnley on course to record their first victory over Blackburn Rovers since 1979.
The former Norwich City defender nodded a Ross Wallace free kick against the post and then reacted first to tuck the rebound home from close range.
Burnley have been good value for their lead and could have been further ahead had it not have been for wasteful finishing by Charlie Austin, who has spurned two good chances.
The game had earlier been delayed after a chicken had found its way onto the pitch.
Stewards eventually removed the bird, which was unharmed.
