Aldridge added nine rebounds and a career-high four blocked shots as Davidson (9-1) improved to 54-15 all-time against the Cougars.
Canyon Barry led College of Charleston (5-6) with 20 points and three steals. Joe Chealy added 19 points and nine rebounds.
Nathan Ekwu's jumper with 3:25 left in the first half gave Davidson a 41-23 lead, but 20 seconds later Chealy converted a three-point play before Canyon hit a 3 to spark a 10-0 run to cut the College of Charleston deficit to eight going into the half.
A pair of free throws by Anthony Stitt and another Canyon 3-pointer pulled the Cougars within 45-41 with 15 minutes remaining.
Aldridge answered with a 3, sparking a 12-4 run and Charleston never again threatened.