Kidd-Gilchrist knocked down a pair of free throws that proved to be the difference with 1:34 to play, and Anthony Davis blocked Carolina's final shot and then secured the rebound to keep the Wildcats (8-0) undefeated.
North Carolina (6-2) had pulled to within one point of Kentucky on a 3-point jumper by Reggie Bullock off a turnover with 50 seconds to play.
The Tar Heels led 43-38 at halftime but put up only 29 points in the second half.
Tyler Zeller and Harrison Barnes led Carolina with 14 points apiece but the team shot 41.7 percent from the field and had 13 turnovers to Kentucky's nine.
Megyn Kelly: Santa Claus and Jesus are both white men
Wisconsin business offering 'therapeutic cuddling' forced to close