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.
Julius Ingram and Jameel Grace scored 11 points each for the Jaguars, and Madut Bol, son of late, former NBA player Manute Bol, added 10 points.