Longwood's leading scorer, Tristan Carey, was held to 1-of-12 shooting, but Woodhouse, who entered averaging 3.7 points, picked up the slack, hitting 6 of 9 shots and all seven free throw attempts.
The game remained close throughout, with 18 lead changes and six ties. Trey Freeman gave Campbell (12-18, 7-8) a 49-48 advantage with a layup midway through the second half but Longwood answered with a 17-7 run over the next six minutes to pull away.
Longwood shot 50 percent (28 of 56) for the fourth straight game.
Andrew Ryan paced Campbell with 16 points.