Goals from Britt Assombalonga and Marvin Johnson as well as an own goal from Matt Clake gave the Teessiders all three points against the Rams.
Our Boro writer Joe Nicholson has dished out his marks following the match – scroll down and flick through the pages of our picture gallery to see them:
9. Duncan Watmore - 7
A few heavy touches early on but asked questions of the Derby defence and assisted the opener with a header across goal. 7 Photo: JPI Media
10. Patrick Roberts - 6
A bright start but held onto the ball for a bit too long at times. 6 Photo: Alex Davidson
11. Britt Assombalonga - 7
Didn’t get many chances but took a first-half opportunity to put Boro ahead. 7 Photo: Alex Pantling
12. Djed Spence - 7
(for Roberts, 62) Made an impact from the bench and provided a driving force on the right. 7 Photo: Getty Images