Nigel Pruitt scored 10 points, Nate Rucker grabbed 10 rebounds, and the Owls (3-4) shot 77.3 percent from the free throw line on 34-of-44 shooting.
Brown scored 27 in the final 20 minutes, with 13 coming at the free throw line.
Casey Jones led the Mocs (3-4) with 22 points and Ronrico White added 10.
The Owls jumped to an 18-6 lead, but the teams were tied at 26 at halftime.
Chattanooga had scoring droughts during both halves, including 6-plus minutes in the second half.