Simmons shot 12-of-22, including 9-of-11 in the first half. The junior guard scored her 1,000th career point by sinking a pair of free throws with 11:44 left in the first half, becoming the 37th Lady Vol to reach that plateau.
Isabelle Harrison added a career-high 18 points to go along with 11 rebounds for the Lady Vols (6-1).
Xylina McDaniel scored 19 points and Waltiea Rolle added 13 points for North Carolina (7-1). The Tar Heels had been allowing only 54.3 points per game and hadn't given up more than 64 points in any of their seven wins prior to Sunday.
The Lady Vols jumped out to a 22-9 lead eight minutes in and never looked back, leading by 21 at the break and by as many as 46 in the second half.
UNC senior point guard Tierra Ruffin-Pratt took a hard fall late in the first half and was unable to play after halftime.
Carolina returns home Wednesday to face Radford at 7 p.m.