Kassim Nicholson added 10 points for the Blazers (5-4).
Montevallo was within 12 points, 51-39, with 15 minutes, 27 seconds remaining in the second half. Later in the half, with UAB leading 57-44, the Blazers went on a brief 7-2 run to extend their lead to 20 points. The Falcons climbed back to within 69-57 with 3:21 remaining, then Benjamin drained a 3-pointer to put the Blazers up by 15 with 2:54 remaining.
Ivan Smith had 14 points for the Division II Falcons. Xavier Malcom and Cedric Jackson added 12 points apiece.
UAB plays North Alabama at home on Tuesday.