Towson fell to 0-13 this season -- and this was only the second time the Tigers have lost by fewer than 10 points.
Virginia had only a three-point advantage with 3:18 to play when Harris hit his long-range shot. Towson came no closer than four the rest of the way.
The Cavaliers (12-1) were led by Sammy Zeglinski with 20 points while Harris had 17. Virginia shot just 34 percent from the field and won the game from the foul line, making 18 free throws to five for the Tigers.
Virginia, the only team from the ACC other than traditional powers Duke and North Carolina to be nationally ranked, opens its league season Jan. 7 against Miami.
Towson got 15 points from Kris Walden. The Tigers' bench provided only two points.
Notable deaths of 2014 [PHOTOS]