Caldwell's dunk gave the Golden Eagles a 78-72 lead with 1:19 left. North Florida's Dallas Moore, who finished with 26, had a layup and nailed two straight 3-pointers to close to 81-80 with 2 seconds left. But Johnson split a pair of free throws to secure the win.
Tennessee Tech trailed 41-32 at the half but shot 63 percent in the second half.
Both teams made 30 shots from the floor but the Golden Eagles were 18 of 24 from the free throw line compared to 10 of 18 for North Florida (6-4).