Brown was 5 of 8 from the floor - including 3 of 4 from beyond the arc - for the Blazers (11-3). Norton was 7 of 8 from the line with seven assists, Dirk Williams scored 11 points and William Lee added 10 points.
Middle Tennessee led much of the first half, and a 10-3 run to close the frame - including 3-pointers by Harris and Xavier Habersham - put the Blue Raiders up 42-30 at intermission.
UAB chipped away in the second half and a pair of free throws by Lee with 5:19 left gave the Blazers a one-point lead. UAB then closed the game with a 14-4 run.