Brown rushed for 295 yards and three touchdowns as Pickens County picked up the 28-0 victory.
Parrish (2-4, 0-4) trailed just 7-0 at the half.
“They basically got all their points on big plays,” Parrish coach Jarrod Wooten said. “They had two touchdowns that went for around 70 yards.”
The Tornadoes opened the game with a 17-play, nine-minute drive to the Pickens County 20-yard line before a fumble ended the drive.
That opening drive set the tone for the Tornadoes, who were held to 150 yards in the game.
Pickens County (6-0, 4-0) gained 312 yards in the game with the bulk going to Brown.
“He carried their team on his back,” Wooten added.
Parrish hosts Brilliant for homecoming next week.