Army's special teams struggled when a blocked punt was recovered by Dominique Cosper in the end zone for another Blazer touchdown to increase the UAB lead to 14-0.
Early in the third quarter UAB scored again on a 50-yard field goal by Nick Hayes.
Army's offense finally got going early in the fourth quarter when Anthony Zurisko kicked a 36-yard field goal to put the Black Knights on the board. Army now trailed 17-3.
The Blazers answered back quickly when Chris Williams scored on a 19-yard touchdown run.
UAB's record improves to 4-5. They host a struggling Tulane (3-6), who have lost their last five.