It was the Rams' final friendly before the Championship campaign starts in one week's time.
The Premier League side took the lead after 31 minutes. Sebastian Larsson whipped in a corner and David Murphy escaped his marker to score with a header.
The visitors extended their advantage in the opening minute of the second half following an awful error by Stephen Bywater.
There appeared to be no danger when Gareth Roberts passed the ball back to Bywater but the big goalkeeper dallied and allowed Larsson to block his eventual attempted clearance and the ball rebounded into the empty net.
Derby reduced the deficit after 58 minutes. Robbie Savage's free-kick was cleared to the edge of the area and Roberts drove an unstoppable shot high beyond Ben Foster's dive and into the top corner.