Bowling Green (15-0) has won five state titles in the last six seasons and set a record for points scored in a Kentucky state championship game.
Carothers led with 128 rushing yards and 111 receiving as the Purples totaled 410 yards of offense.
Bowling Green ran away with 48 unanswered points in the second half to break a 22-22 tie at halftime.
The Purples scored three fourth-quarter touchdowns on a 71-yard interception return for a touchdown, a 58-yard punt return and a strip fumble on a kickoff taken into the end zone for a score.
Clark Payne threw for 278 yards and two touchdowns, and Deangelo Wilson had two scores for the Purples.
Bowling Green is now 3-0 since 2013 against Pulaski County in the state finals. Wiley Cain led Pulaski County (12-3) with 187 yards passing and two TDs.
