Junior Casey Johnston had nine points and sophomore Lincoln Skaggs added eight as the Cougars (4-1) pulled away from the scrappy Panthers (1-5) in the fourth period.
It was the timing of the points that was most important for Grayson County. Skaggs scored all of his points in the second half, when the Cougars built a lead, then had to hold off a late Panther rally. Johnston scored seven of his points in the second half.
Grayson County trailed in the early stages of the opening period, but closed with a 7-0 run that gave them an 11-8 lead heading into the second quarter.
Sophomore Chase Richardson, who finished the contest with a game-high 15 points, hit a 15-foot jumper at the beginning of the period to give the Cougars a five-point lead,
The Panthers battled back to tie the score with 2:48 to go in the half, but the Cougars held a 16-15 lead at the break.
Grayson County took charge in the third period by outscoring the Panthers 11-3, including the last seven in a row, and led by nine, 27-18 as play began in the fourth quarter.
The Panthers came out with renewed fire, putting together an 11-2 run that tied the score at 29-29 with 3:58 left in the game.
Richardson put the Cougars back on top with a three-point play at the 3:27 mark, but the Panthers tied things one more time with 2:22 to play.
With 1:26 left, Jon Meredith came up with a big steal and fed Skaggs all alone under the basket for a layup that put Grayson County on top for good.
Daviess County called a timeout, then promptly turned the ball over. Richardson found Skaggs at the other end for a short jumper and the Cougars led by four with 42 seconds left.
The Panthers missed, then Richardson capped things with a rebound basket with 23 seconds remaining and the Cougars cruised to the win.