The Volunteers (10-2) will face Charles Henderson (12-0), which beat Childersburg 35-0.
Clay Central rushed for 307 yards and took a 16-0 lead going into halftime after Jaylon Lyles scored on a 4-yard run in the first quarter.
JoJo Staples scored on a 4-yard run, which was set up by a 94-yard run by Lyles in the second quarter.
In addition, the Volunteers’ defense forced a safety.
Bibb County started the second half by scoring its only touchdown of the game.
Clay Central responded with Deidric Rutledge scoring on a 61-yard run to seal the deal in the second-round contest.
Lyles rushed for 209 yards on 24 carries, passing the 2,000-yard mark for season. He sits at 2,055 yards. Rutledge had 71 yards on five carries.
The Clay Central defense intercepted five passes.