Chuba Akpom scored the only goal of the game shortly after half-time before James Collins saw a penalty disallowed for Luton and Sam Morsy was sent off for the hosts.
Our Middlesbrough writer Joe Nicholson has dished out his marks from the match – scroll down and flick through the pages of our picture gallery to see them:
1. Marcus Bettinelli - 5
Didn’t have much to do and almost cost his side when he spilled a long-range shot which led to a Luton penalty. Made an excellent save late on though. 5 Photo: Alex Pantling
2. Anfernee Dijksteel - 7
Made a few forays forward in the first half and saw out his defensive duties as Luton applied the pressure. 7 Photo: Getty Images
3. Paddy McNair - 8
Delivered a few dangerous set-pieces and read the game well at the back as Boro’s defence stood firm. 8 Photo: Alex Pantling
4. Dael Fry - 8
Made a crucial block after Boro went down to ten men and was commanding in the air throughout. 8 Photo: PA