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.
ESPN's Dan Dakich joins The Paul Finebaum Show to discuss the SEC's presence in the NBA Draft.
Ted Kapita was the top-rated recruit from West Virginia in the class of 2015 and recently played at DME Academy in Florida.
With the Suns drafting Tyler Ulis, they now have five guards on their roster who attended Kentucky.