With the Hornets (4-10, 1-4 ODAC) leading 29-26 following an Olivia Callan jumper in the lane 51 seconds into the third quarter, Bridgewater (8-6, 1-4) reeled off 16 of the game's next 20 points to take a lead it would not relinquish.
The run, which took 6:22, gave the Eagles a 42-33 lead with 2:30 remaining in the stanza.
Shenandoah responded with an 8-2 run of its own around the third quarter break to cut the deficit to three, 46-43, but would get no closer.
Junior Kirstyn Arcata, who had a team-high 13 points for the Hornets, brought SU to that three-point deficit with consecutive layups at 9:21 and 7:51.
Bridgewater then closed out the contest on a 10-5 run to provide the final margin of victory.
The Eagles strong second half capped a game win in which the two teams traded the lead three times and were tied on five additional occasions.
In the first half, the two teams were never separated by more than four points.
In addition to Arcata's 13, Callan had 11 points for the hosts.
Briana Moore had a game-high 17 for BC with Jessica Lam adding 12.
Bridgewater had a 47-38 advantage on the glass which led to 14-7 bulge in second-chance points.
SU shot 32 percent to 30 percent for the Eagles.
The women are back in action on Saturday at 2 p.m. in an ODAC contest at Randolph.