The 37-point margin of victory was the largest in coach Tony Bennett's time at Virginia.
"We tried to challenge our team and make (S.C. State) earn everything," Bennett said. "We didn't know a lot about the opponent we were playing, but we knew we were going to guard them and play man-to-man.
"The battle cry for us is to just limit the shots and limit their offensive rebounds. Our guys worked hard and plugged the gaps. There was one part where they got a little lackadaisical, but they had the right kind of mindset and spirit of execution on the defensive end."
Virginia shot 49 percent (25 of 51) and held South Carolina State to 25.5 percent shooting (13 of 51).
Harrell, who went 1 of 6 in the first half, came out blazing to start the second, drilling three consecutive 3-pointers to give Virginia a 47-20 lead. The Cavaliers led by as many as 40, and outrebounded the Bulldogs 44-29.
"I just want to be as consistent a 3-point shooter as I can," said Harrell, who tied a career high with his three 3-pointers, "because my money shot, so to say, is my mid-range shot.
"So if I can get defenses to close out a little bit harder on my 3-point shot, then I'll be able to get my mid-range shot (easier)."
The Cavaliers, who led 33-18 at halftime, missed their first seven shots in the first three-plus minutes before quickly finding their groove.
Scott, who missed last season with an ankle injury, scored Virginia's first points on a two-handed put-back dunk that got the crowd fired up and ignited a 9-0 run.
Omar Sanders led South Carolina State (1-1) with 13 points.