The homestanding Cougars trailed 2-0 after the Panthers got a pair of runs in the top of the first.
But LCHS tied the game on a two-run homer by John Logan Dockins in the bottom of the first.
Logan County then got three runs in the bottom of the third to take its first lead of the game.
Russellville wasted no time tying the score, however. D.J. Watkins knotted the game with a three-run homer in the top of the fourth.
Logan County went up 6-5 in bottom of the fourth and that's where the score remained for the remainder of the game.
Lawton Jackson pitched a complete game for LCHS to earn the win. Darrin Murphy pitched the complete game for RHS.
Earlier this season, Russellville beat Logan County 12-2.
Logan County is now 10-10 overall and 3-2 in District 13 competition. Russellville leads the district at 4-1 and LCHS is second.