Johnson has scored 20-plus points in three straight games - and in five of his last seven.
Clinging to a 56-54 lead with a little more than 12 minutes remaining, Johnson scored 10 straight Winthrop points - on two 3-pointers, a layup and two free throws - to make it 66-59 with 8:37 to play.
Then with 2:32 left, Gavin made layups on two straight drives for a 13-point lead. Georgia Southern scored the next seven points, but Gavin, Josh Davenport and Johnson combined to make 6 of 6 free throws in the final 46 seconds.
Tookie Brown led the Eagles (3-6) with 25 points.