Also in double figures for the No. 13 Tar Heels were freshman forward La'Tangela Atkinson (13 points) and senior guard Coretta Brown (11 points). Junior center Carrie Davis added a career-high nine points in 14 minutes off the bench.
Junior forward Courtney Laird and junior guard Robyn Flewelling led Davidson with 10 points each. Senior forward Bethany Schott grabbed a game-high 10 boards as the Wildcats outrebounded UNC 44-43.
"Rebounding is the biggest thing we have to improve," UNC coach Sylvia Hatchell said. "We got outrebounded, and we can't allow that to happen. I also thought there were times that we didn't take care of the ball."
The Tar Heels committed 18 turnovers while handing out 18 assists. Davidson had 29 turnovers and 11 assists.
Carolina scored the first six points in the game, but the Wildcats kept the margin close throughout the first half and led by three with 3:25 to play before the break. Both teams struggled from the floor, UNC shooting 36.7 percent (11-30) and Davidson 27.3 percent (9-33) en route to a 28-25 halftime lead for the Tar Heels.
"I thought we played well in the first half," Davidson coach Annette Watts said. "We're a young team and not as deep as Carolina, and I knew that would hurt us in the second half."
After the break, UNC hit its first five field goals to open up an 11-point lead. Sutton scored 14 of her points on 6-for-8 shooting in the second half, with eight points coming in a 30-second span when she converted back-to-back three-point plays. The Tar Heels shot 41.7 percent in the second period and led by as many as 27 points.
"In the second half, I thought we had a few times when we looked really good, but it was off and on," Hatchell said. "I did think the freshmen, La'Tangela Atkinson and Jessica Sell, played well in their first game."
The Tar Heels will return to action less than 48 hours after their first game when they host East Tennessee State on Sunday at 2 p.m. Carolina departs on Monday morning for the Rainbow Wahine Classic in Honolulu, Hawaii., where the Tar Heels will play three games in three days, beginning with a matchup against DePaul on Nov. 29.
"We just want to get better, get on the boards better, correct what we did wrong tonight," Hatchell said. "Playing these first two games so close together should help us prepare for our tournament in Hawaii."