The Hornets scored three runs in the top of the first but trailed after one as Bridgewater (23-17) answered with four in its half of the frame.
A two-run third gave SU the lead for good but coach Marlena Kotynski's club needed one run in the fourth, two in the fifth and one more in the seventh to hold off the Eagles.
Senior Carrie Robinson (9-10) went the distance, allowing the seven runs on 10 hits and three walks while striking out two.
After giving up three runs in the sixth, Robinson retired BC in order in the seventh.
Allie Schey had what proved to be the game-winning RBI with a two-out bases loaded double into the gap in left-center in the top of the fifth.
Schey's hit chased Bridgewater starter Brooke Louden (10-5), who was tagged with the loss after allowing eight runs (four earned) on 11 hits and one walk in 4 2/3 innings.