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:
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Patrick Roberts playing for Sunderland against Birmingham. Photo: Frank Reid
. Anthony Patterson - 8
Had an excellent game, made a couple of smart stops, swept up off his line well and defended his box well late on. 8 Photo: Martin Swinney
. Lynden Gooch - 6
Had a difficult task up against Khadra, one of the quickest players in the league. Did OK, and was very close to an early assist when Pritchard almost converted his cross. 6 Photo: Frank Reid
. Trai Hume - 7
His first Sunderland goal has been a while coming and a reward for his continued excellence in the air. Did well when Sunderland opened up in search of the winner in the second half. 7 Photo: Frank Reid
. Danny Batth - 6
One or two uncomfortable moments in possession but a strong header from a corner to get Sunderland back level just before the break. 6 Photo: Frank Reid
1. Anthony Patterson - 7
His passing was calmer and more precise than some of the outfield players and he made one excellent stop late on to prevent it becoming a nervy finish. 7 Photo: Frank Reid
2. Trai Hume - 6
Started superbly but grew frustrated by some of the inconsistent refereeing on show. Played his part in a good win in the end. 6 Photo: Frank Reid
3. Jenson Seelt - 6
Played some good passes and very incisive switches of play, though was caught out by the tempo of the game and the Birmingham press at times. Much better in thes second half and will be better for his full league debut. 6 Photo: Frank Reid
4. Nectarios Triantis - 6
Played an important part in the second goal, applying the pressure on Aiwu that forced him to turn into his own goal. One or two dangerous defensive moments but came through his league debut OK. Will be a boost for Mowbray, who knows he can trust this pair when needed next. 6 Photo: Frank Reid