In-form Clarets striker Charlie Austin headed in Kieran Trippier's teasing cross after two minutes for his third goal in four games this season.
But Cardiff hit back five minutes before the break when veteran Robert Earnshaw fired in low from six yards.
Neither side could find a winner, though winger Keith Treacy went close as the hosts pressed hard for victory.
Burnley started the match the brightly with defender Trippier engineering the space to flight a cross into the heart of the Bluebirds' penalty box, which Austin arrived to head home from six yards out.
Cardiff gradually steadied themselves and almost drew level when Mark Hudson arrived to meet a cross, only to see his close-range header flash narrowly past the goal.
Burnley almost doubled their lead 11 minutes in when Trippier again found space to cross but Austin steered his header wide.
After Treacy flashed a 12-yard shot just wide, the visitors drew level in the 40th minute when defender Andrew Taylor set up Earnshaw to score his 200th club career goal with a simple left-footed finish
Again, Treacy threatened for Burnley - this time with a 12-yard strike - before Cardiff defender Kevin McNaughton blocked well late on from Burnley substitute Zavon Hines.