On top 39-34 at halftime, Eastern Kentucky opened the second half on a 15-6 run to go up 54-40 with 14:37 left to play.
The Colonels took their biggest lead of the game, 65-46, on Johnson's layup with 9:01 remaining.
Brian Williams' 3-pointer cut Jacksonville State's deficit to 71-67 with just under 2 minutes to play, but the Gamecocks failed to score another point.
Eastern Kentucky shot 53.6 percent (15 of 28), while Jacksonville State shot 42.3 percent (11 of 26), in the second half.
Tarvin Gaines led the Gamecocks (15-10, 7-7) with 21 points.