BBA (6-4) led 14-6 at halftime after scoring on its first two possessions. Chris Redding had a 12-yard scoring run and Eric Cerra caught a seven-yard screen pass from quarterback Jake Stalcup for the other score.
The Bulldogs were unable to capitalize on three Rice (10-0) turnovers in the first half.
Stalcup was limited to 162 yards on 13-of-28 passing. The Green Knights poured on 30 unanswered points after halftime behind the strong running of Casey Tipson (134 yards) and Billy O'Brien (121 yards).
Rice, the 2010 state champion, advances to the D-II final this Saturday against second-seeded Bellows Falls.