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:
13. Jewison Bennette (sub) - 6
Brought real energy through the final third and it asked some questions of Luton - will have a bigger role to play after the international break. 6 Photo: Frank Reid
14. Alex Pritchard (sub) - 6
Still working his way back to full speed but had some decent moments. Sunderland finished the game very strongly and he was part of it. 6 Photo: Frank Reid
15. Lynden Gooch (sub) - 6
Did well down the left flank, beating his man a few times and playing some dangerous crosses. 6 Photo: Frank Reid
16. Pierre Ekwah (sub) - 6
One of his better cameos, moving the ball quickly and dropping onto second balls well. 6 Photo: Frank Reid