Britt-Black had 11 points and 10 rebounds and Justin Patton added 11 points for the Tigers, who snapped a four-game losing skid.
The Tigers (3-12, 1-2 Southwestern Athletic Conference) shot 51.5 percent (17 of 33) in the first half, including 5 of 10 from 3-point range, and led 40-20 at halftime.
Grambling State led by as many as 22, 46-24, on Rupert Rose's layup with 16:39 left to play.
The Jaguars (2-13, 1-2) then answered with a 24-6 run. Brandon White's free throw brought it to 52-48 with 5:35 remaining. However, Southern wouldn't get any closer than four the rest of the way.