The Blazers (8-2), coming off the longest layoff in program history at 14 days, trailed 18-17 at halftime.
With the Bulldogs (3-5) ahead 23-19, UAB used a 14-0 spurt, including seven points from Moore, to lead 33-23.
Alabama A&M's scoring drought, which lasted 4:02, ended with a 3-pointer by Desmond Jackson, who paced the Bulldogs with eight points.
UAB led by as many as 23 in the second half.
Neither team shot well in the first half, but the Blazers improved to 45.2 percent in the second (14 of 31), while the Bulldogs shot only 34.6 percent (9 of 26).
UAB's Aaron Johnson, who leads the country in assists per game (8.2), had eight assists.
The Blazers are 7-0 all-time against the Bulldogs.