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:
9. Duncan Watmore - 5
Started through the middle and switched to the right in the second half but struggled to make an impact. 5 Photo: Getty Images
10. Marcus Tavernier - 7
Provided the moment of quality for Boro’s opener after a direct run which created space for Johnson and Akpom to combine. 7 Photo: George Wood
11. Chuba Akpom - 6
Hardly touched the ball in the first half but was alert to score the opener shortly after the break. 6 Photo: Getty Images
12. Lewis Wing - 6
(for Watmore, 70) Came on after Morsy’s red card and helped Boro see out the win. 6 Photo: Alex Burstow