Sean O’Driscoll’s team were without injured trio Billy Sharp (ankle), James Hayter (knee) and Ryan Mason (ankle) after they picked up injuries in the first two Championship games of the season.
Chelsea forward Milan Lalkovic arrived on loan from the Premier League club to bolster Doncaster’s attack, while defender Reece Brown - brother of Wes Brown - joined in a short-term deal from Manchester United.
Both loan players were handed their full debuts at Derby but it was veteran Kevin Kilbane who put the Rams in front after five minutes, heading home a corner.
And it got worse at the start of the second half as Steve Davies struck a second goal for the hosts.
A County third came from Ben Davies, who set-up the first two goals, after good work from Lee Croft.
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