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.
SMU has signed a second player from Australia, 6-foot-11 forward Harry Froling, to a national letter of intent. The Mustangs previously signed guard Tom Wilson from Australia.
There's nothing to suggest the Jayhawks won't end up atop the Big 12 for a 13th season in a row. But what about a return to the Final Four?
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.