The home side had the first real chance in the 13th minute when Connor Sammon's deep cross found Robinson, who could only sidefoot wide.
Blackburn took the lead ten minutes before the interval when Jordan Rhodes swept a volley home from the edge of the area after Derby failed to clear.
Rovers begun the second half on top but it was Derby who created the first opening after the interval when Jeff Hendrick crossed for Craig Bryson, who could only smash over.
Paul Coutts then curled an effort that beat Paul Robinson but not the crossbar as Derby continued to press for a leveller.
Derby got their equaliser minutes from the end as Bryson's shot was parried straight into the path of Robinson, who made no mistake from close in.