The Black Cats fell a goal down in the 29th minute when George Hall converted a close-range chance for the visitors.
Sunderland responded, though, as Trai Hume equalised on the stroke of half-time, before Amad put his side ahead 15 minutes from the end.
The hosts were forced to hang on in the closing stages after a red card for Dennis Cirkin, but managed to claim all three points.
Here’s how Phil Smith rated the Sunderland players against Birmingham:
5. Niall Huggins - 8
Sunderland’s man of the match, in my opinion. A threat going forward and stood up to help a very inexperienced defence with some crucial interventions. Hugely impressive. 8 Photo: Frank Reid
6. Dan Neil - 6
Had a strong second half and was denied only by a good Ruddy save at one stage. Took time to get to grips with Birmingham’s pressing but came through. 6 Photo: Frank Reid
7. Pierre Ekwah - 5
Had a very difficult second half in which he often gifted up possession in the face of Birmingham’s aggressive press, and it could have left his side behind. Much better in the second half. 5 Photo: Frank Reid
8. Patrick Roberts - 7
Played a part in Sunderland’s second goal, his cross to the back post for Hume forcing the own goal. Another of the ‘second assists’ that Mowbray points to as a sign of his ongoing importance. Dangerous throughout and a relief that he was able to run off what initially looked like a muscle injury. 7 Photo: Frank Reid