Visitors Rotherham could have been forgiven for thinking there was every chance that they could have heaped more misery on the cash-strapped Rams - but found themselves the light relief after goalkeeper Mike Pollitt fell foul of a debatable decision.
Pollitt dropped onto a loose ball which TV replays showed was just inside the area but referee Dunn brandished a red card after deeming the "offence" to have taken place outside the penalty area.
Georgi Kinkladze added insult to injury by curling the free-kick into the top corner to leave Rotherham both a man down and a goal in arrears after just 15 minutes.
It proved to be the turning point as the match was transformed into a glorified training session with the hosts endeavouring to break down the Millers defensive formation.
And given such licence to dominate midfield, Kinkladze produced one of his most domineering displays in a Derby shirt as he ran riot for the rest of the game.
One of any number of slide rule passes set up Izale McLeod on 37 minutes only to see substitute keeper Ian Gray pull off a smart stop.
But minutes later he threaded an identical ball through to midfielder Adam Bolder and this time the resulting shot was despatched powerfully into the bottom corner.
Any hopes that the massed ranks of visiting fans had of a second-half comeback were snuffed out inside four minutes as Kinkladze ushered Warren Barton down the inside right channel and his low cross was clinically turned in by McLeod at the near post.
Chances galore fell to the home side with Lee Morris striking the ball, side netting, and goalkeeper and Kinkladze and substitute Fabrizio Ravanelli also coming within inches of extending the lead.
Poor Rotherham only managed one shot on target in the last minute and were left ruing the referee's intervention at such an early juncture.