Boro fell two goals behind in the first half at Pride Park after goals from strikers Lee Gregory and Colin Kazim-Richards.
The visitors did manage to pull a goal back before the break through Neeskens Kebano but weren’t able to build momentum after the interval.
Neil Warnock’s side have now gone five games without a win and slipped six points adrift of the Championship play-off places.
Boro will now hope to get back to winning ways when they host Huddersfield on Tuesday – but will have to manage without new signing Yannick Bolasie.
The winger missed the Derby match with a hamstring issue and is set to be sidelined for a while.
Our Boro writer Joe Nicholson has dished out his marks from the fixture – scroll down and flick through our gallery to see them:
5. Marc Bola - 6
Made a few forays forward from left-back and assisted Boro’s goal when his cross deflected into Kebano’s path. 6 Photo: Alex Burstow
6. Jonny Howson - 5
Slow to react at times in midfield. Moved into a more advanced role when Boro were chasing the game but struggled to make an impact. 5 Photo: George Wood
7. Sam Morsy - 5
Tried to close players down and offer energy but never really got to grips with the game. 5 Photo: Getty Images
8. George Saville - 4
Game passed him by and the midfielder was substituted in the second half. 4 Photo: Getty Images