Copperas Cove, which lost in the finals for the second straight year, led 7-0 at halftime when Josh Boyce scored on a 4-yard run with 36 seconds left in the second quarter.
Rodgers, who has orally committed to Oregon State, went to work in the second half, scoring on runs of 31, 8 and 87, the last giving Lamar Consolidated (13-2) a 20-7 lead with 2:43 left in the game. He had 31 carries.
Rodgers' long touchdown came after Copperas Cove quarterback Robert Griffin was stopped at the Lamar Consolidated 2 on fourht-and-goal by Lamar Consolidated's Chuck Obi and Cory Green.
Copperas Cove (12-3) managed a late score on a 2-yard run by Brandin Byrd with 59 seconds left, but Obi recovered the onside kick.
Lamar quarterback D.J. Smallwood added 103 yards rushing on 19 carries and completed three of eight passes for 44 yards.
Robert Griffin led Copperas Cove with 91 yards rushing on 18 carries and was 9-of-16 passing for 117 yards. Boyce had three catches for 58 yards.