Shenandoah (6-4, 2-4 ODAC) battled hard in doubles, dropping close matches in all three contests to spot the Eagles (9-4, 6-1) a 3-0 lead.
Bridgewater then swept the six singles matches in straight sets.
The closest singles match came at No. 6, where Kris Stokes outlasted Evan Rosenberg 6-3, 7-5.
In doubles, Zack Frack and Bryan Harris fell 8-6 at No. 2 to Stokes and Emmett Johnson.
The men are back in action on Sunday at 2 p.m. in a non-league senior day match versus Stevenson.