Derby, who had won eight out of their last nine games, dominated the early possession with skipper Matt Oakley forcing the game's first save from Clarets keeper Danny Coyne.
Coyne then produced a fine save on his near post to deny Oakley again after a neat interchange of passes between Jon Stead and Steve Howard.
But it was the home side that should have gone in front with the game's best chance as Wade Elliott set-up Gifton Noel-Williams, only for the striker to head straight at Derby keeper Stephen Bywater.
Burnley's injury crisis worsened with Coyne forced to leave the game and be replaced by substitute Brian Jensen.
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James O'Connor tested Bywater early in the second half after Noel-Williams and Kyle Lafferty had combined well.
After being sent clear down the right by Noel-Williams, Burnley right-back Wayne Thomas crashed a low cross in for Chris McCann, who just missed the target at the near post.
At the other end Barnes should have done better than pull his shot wide from the edge of the box.
Lafferty then rolled the ball along the six-yard line but there was nobody in a Claret jersey to apply the finishing touch.
Derby boss Billy Davies replaced skipper Oakley with Morten Bisgaard and striker Stead with Arturo Lupoli. The on-loan Arsenal player missed a great chance to score with his first touch.
But, at the end of 90 competitive minutes, both sides will feel that a point was a fair result from this fixture.