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:
5. Marc Bola - 7
Another solid performance at left-back as Boro were rarely threatened on the flanks. 7 Photo: Alex Dodd - CameraSport
6. Sam Morsy - 5
Gave Boro protection in midfield before he was harshly sent off for handball. 5 Photo: Alex Pantling
7. George Saville - 7
Didn’t offer as much going forward but was full of energy again and helped cover ground when Boro went down to ten men. 7 Photo: Getty Images
8. Marvin Johnson - 6
Quiet in the first half but claimed another assist and saw out his defensive duties before he was substituted in the second half. 6 Photo: George Wood