Tosin Mehinti scored 13 points and Hakeem Baxter added 10 for the Blazers (6-9, 2-0 Conference USA), who shot 44.4 percent from the field. William Lee contributed seven points with 11 rebounds, leading to a 42-31 advantage on the boards for UAB.
UAB led 52-44 with nine minutes remaining, but the Owls reeled off a 13-4 run to grab the lead on Lacunza's 3-pointer with 3:23 left. Brown followed with his jumper and Lee dunked on a putback for a 60-57 lead with 55 seconds left.
Baxter sank four late free throws as FAU finished cold, missing its last seven attempts after Lacunza's 3.