After a goalless first half, the visitors took the lead six minutes after the restart when Alfie Doughty’s low effort beat goalkeeper Anthony Patterson.
Sunderland reacted well, though, with Mowbray using all five of his available substitutes.
One of those subs then won a penalty as Amad was fouled in the Luton box, before converting from the spot.
Here’s how Phil Smith rated the Sunderland players against Luton:
. Safc Ltfc O'Nien Fouled 1.jpg
Luke O'Nien playing for Sunderland against Luton. Photo: FRANK REID
. Anthony Patterson - 4
Will be so frustrated with the opener, albeit the effort came through a crowd of bodies and he saw it very late. A rare error in what has been an excellent season. 4 Photo: Martin Swinney
. Trai Hume - 6
Defended well and moved into midfield to offer an option on the ball well at times. Steady enough. 6 Photo: Frank Reid
. Daniel Ballard - 9
Completely dominated his duel with one of the best strikers in the division this season, Carlton Morris. So aggressive in all of his decisions and rarely lost out, either. 9 Photo: Frank Reid
. Danny Batth - 7
Part of a defence that deserved a clean sheet, really. Very good in the air and defended well in possession, was left frustrated that what appeared a pretty soft free kick against him led to Luton’s goal. 7 Photo: Frank Reid
. Luke O’Nien - 8
Defended well and fed Clarke excellently with some precise passing. Has done really well at left back, and has a big future in this backline. Deserved to be on the winning side. 8 Photo: Frank Reid
1. Anthony Patterson - 4
Will be so frustrated with the opener, albeit the effort came through a crowd of bodies and he saw it very late. A rare error in what has been an excellent season. 4 Photo: Martin Swinney
2. Trai Hume - 6
Defended well and moved into midfield to offer an option on the ball well at times. Steady enough. 6 Photo: Frank Reid
3. Daniel Ballard - 9
Completely dominated his duel with one of the best strikers in the division this season, Carlton Morris. So aggressive in all of his decisions and rarely lost out, either. 9 Photo: Frank Reid
4. Danny Batth - 7
Part of a defence that deserved a clean sheet, really. Very good in the air and defended well in possession, was left frustrated that what appeared a pretty soft free kick against him led to Luton’s goal. 7 Photo: Frank Reid