Krista Gross, who ranks second in the Atlantic Coast Conference in rebounding, pulled down a career-high 17 for North Carolina, which bounced back from a 102-57 loss to No. 14 Tennessee on Sunday.
North Carolina (8-1) opened the game on an 11-2 run, and after Jordynn Gaymon's jumper cut the deficit to 13-4, the Tar Heels scored the next eight points to lead 21-4 with 4:19 left in the first half.
They led 33-10 at the break and went up 46-23 in the second half behind a jumper from McDaniel.
North Carolina out-rebounded Radford 52-27 and improved to 144-13 in games in which it has won the rebounding battle dating to 2006.
Diani Mason led Radford (3-4) with 10 points.