Shorter had not lost at home in more than two years, dating back to Jan. 15, 2011.
Shorter’s Kenny Leverette scored a game-high 22 points, going 5-for-9 from the field and 12-for-13 from the free throw line.
The Chargers, who are in first place in the Gulf South Conference, jumped out to a 40-31 lead at the half by shooting 43 percent from the floor, including making seven 3-pointers.
Shorter (12-5, 6-3 GSC) drew as close as three points in the second half, 57-54, but could not complete the comeback.
Brandon Pullman scored 15 points off the bench, connecting on three 3-pointers, while also grabbing seven rebounds.
Brandon Wright added 10 points, and Dedric Ware had nine points and five boards.
UAH (14-3, 7-2 GSC) made 12 three-pointers.
“Let’s give UAH credit, they were better than we were,” said Shorter coach Chad Warner. “The were very well prepared and played hard. I was extremely proud of our team’s effort. We will go back to work on West Alabama on Monday.”
The Hawks visit West Alabama on Thursday.