Keith Bertschin's side sailed into a three goal lead with goals from Krystian Pearce, Garry O'Connor and Mikael Forssell.
However five minutes into the second period Jon Macken pulled one back for the visitors and when Matt Richards netted on 73 minutes Blues were forced to defend for their lives to hold on for maximum points.
Blues Res: Doyle, Parnaby, Sadler, Martin Taylor, Pearce, Mutch (Burge, 83), Dann's, Howland, O'Connor, Forssell, Milojevic.
Derby County Res: Hinchliffe, Edworthy, Camara, Johnson, Adison, Malcolm, Holmes, Richards, Macken, Beardsley, Simmons (Ujcik, 84).