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:
5. Marc Bola - 7
Kept the attack alive which led to Boro’s second goal. Made a few forays forward. 7 Photo: Clive Brunskill
6. Jonny Howson - 8
Produced a fine cross for Boro’s opener. Tenacious in the engine room as Boro wrestled control of the contest. 8 Photo: Getty Images
7. George Saville - 8
Snapped into challenges and prevented danger. A tireless display in midfield. 8 Photo: Getty images
8. Marcus Tavernier - 7
Started on the right and produced some probing runs. Will be disappointed he didn’t score after his second-half effort was saved. 7 Photo: Getty Images