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:
13. Marvin Johnson - 8
(for Watmore, 62) A goal and an assist from the bench. Added Boro’s third with an excellent effort. 8 Photo: George Wood
14. Chuba Akpom - N/A
(for Assombalonga, 72) Came on in the closing stages. N/A Photo: Getty Images
15. Lewis Wing - N/A
(for Tavernier, 88) Made a late cameo. N/A Photo: Alex Burstow