The loss comes in the first-ever ODAC football game for Shenandoah (1-3, 0-1 ODAC).
Freshman John Griggs nailed what proved to be the game-winner for BC (3-0, 1-0), hitting a 33-yarder from the right hash with 8:47 to play.
Bridgewater only drove nine yards on the drive that ended with the Griggs field goal and was set up with excellent field position thanks to a 23-yard Antonn Briley punt return that set the hosts up with a 1st and 10 from the Hornets 25.
The Eagles gained one first down on the drive before losing a total of three yards on the next three plays.
Griggs split the uprights with his field goal.
Shenandoah forced BC into taking that attempt by taking the score at 14-14 on a Corey Taylor 1-yard TD run on the first play of the fourth quarter.
Taylor's TD run, his second of the day, was set up by a Brandon Martin interception that gave SU a first down on the Bridgewater 3.
Andrew Smith gained all but a foot of what SU needed on the first-and-goal play, setting Taylor up to score on second down.
Taylor's first score, which tied the game at 7-7, came on a 14-yard run up the middle and capped a 10-play, 71-yard drive.
The Eagles answered that score with one of their own, as Shawn Lee hauled in a 63-yard Willie Logan pass on 3rd and 19 to put the hosts back up again by a touchdown.
The Shenandoah defense once again played well, holding BC to just 55 yards rushing on 40 attempts. The Eagles had 121 of their 261 yards passing on three plays.
Jujuan Johnson had 12 tackles and Josh Rogers nine for the Hornet defense.
SU is off next week and hosts Guilford in an October 6 Homecoming contest.