Martin Hankins threw for 298 yards and Duke Calhoun led Memphis receivers with 159 yards on four catches, including a pair of 70-yard receptions.
UAB's scores came on a 26-yard field goal by Swayze Waters , and a 1-yard run by Brandon Thornton , the first rushing touchdown by a Blazer running back this season.
Sam Hunt completed 11-of-19 passes for 121 yards for UAB (2-9, 1-5 Conference USA).
Memphis (6-5, 5-2) held a 13-3 lead at the break behind a pair of field goals by Reagan and a 1-yard touchdown run from reserve quarterback Will Hudgens .
Hankins, who had thrown for an average of 406 yards over the previous two games, completed 9-of-18 for 197 yards in the first half. The Tiger running attack, almost nonexistent in recent weeks, managed 106 yards in the first half, and finished with 265 rushing for the game.
The Blazers switched quarterbacks between Joseph Webb and Hunt. The pair combined to complete 10-of-14 passes in the half for 82 yards, as UAB managed only 147 yards of offense before the break.
Reagan would add field goals of 24 and a season-high 38 yards in the second half.
Memphis is bowl-eligible for the fourth time in five years.