The 17th-ranked Seminoles (24-9) were led by Michael Snaer, who scored 18 points, and Deividas Dulkys who added 16.
Florida State notched a 58.9-percent shooting percentage from the field and hit half of its 22 attempts from 3-point range.
North Carolina (29-5) shot 39.4 percent from the field but outrebounded the Seminoles 37-26.
Harrison Barnes led Carolina with 23 points and Tyler Zeller had 19 points and a dozen rebounds.
Kendall Marshall hit a 3-pointer for the Tar Heels that cut Florida State's lead to 83-82 with 32 seconds to play but he missed a second try with 10 seconds remaining.