Michael Chopra sold two Derby defenders a dummy to slot home the opening goal after 15 mins but Derby levelled on 25 mins when Tomasz Cywka got his toe to the ball ahead of the City defence.
The game was held up for a long while just before half time when Kevin McNaughton took a nasty blow. He was taken to hospital but thankfully was allowed home later in the evening after suffering concussion.
Burke secured the points in the 2nd half when he tapped into an empty net after the Derby defence made a hash at clearing the ball.
No Koumas today but high praise for Olofinjana who made his debut.