Derby went in front on the half-hour mark with a blistering 30-yard free-kick from flamboyant Spaniard Inigo Idiakez but were then hit by an early second-half blitz which saw the Clarets storm in front thanks to goals from strikers Ade Akinbiyi and Gifton Noel-Williams.
The game was turned upside down again when the home side lost central defender Wayne Thomas to a straight red card following an aerial challenge on Rasiak.
Visitors boss Phil Brown was then banished to the stands by the referee for twice infringing his technical area as passions rose at Turf Moor.
Derby right-back Marc Edworthy suffered a serious accidental injury which resulted in the game being stopped for eight minutes whilst he received attention.
In total there were 11 minutes of stoppage time added to the game during which Rasiak headed home a cross from Tommy Smith to preserve Derby's unbeaten record.