Strikes at the beginning and the end of the first half proved enough to earn Rovers the win.
The home side got off to the perfect start, when Rhodes sent Frank Fielding the wrong way from the spot having won the penalty himself.
It took a while for the game's next opportunity to unfold, but Rhodes's volley was comfortably saved by Fielding following Colin Kazim-Richards chest-down in the 23rd minute.
Rovers keeper Grzegorz Sandomierski was forced into a stunning save on the half-hour mark, when Jamie Ward found Chris Martin with a free kick, but the former's header was superbly stopped at the near post.
However, the hosts doubled their lead on the stroke of half time when Dann headed in from a corner by David Jones.
After the break, Blackburn had a great chance to seal the win when Rhodes was played through on goal from a Sandomierski clearance; he brought the bouncing ball under control before Fielding came out to save the effort.
Derby nearly got on the scoresheet in injury time, but Sandomierski was on hand to keep out Ward from close range.