Johnson, who finished with 12 points and 14 rebounds, helped the Bulldogs (10-11, 5-4 Mid-Eastern Athletic Conference) shoot 54.9 percent from the floor (28-for-51). Westley Telfare and Jason Flagler each had 12 points.
The Eagles (7-16, 5-5) took a 52-49 lead on Sam Coleman's jumper with 10:04 left in the second half. But South Carolina State went on an 8-0 run over a two minute stretch, claiming a 57-52 advantage with 7:25 remaining.
After Coppin State's Brian Chestnut made a layup with 4:25 left, the Eagles were held scoreless for the next four minutes. Johnson's three-point play with 1:12 left made the score 69-58.
Tywain McKee scored 15 points for Coppin State, which shot 39.3 percent.