North Carolina scored the final seven points of the first half to take a 38-31 lead at the intermission, but Davidson hung in throughout the second half. Andrew Lovedale grabbed an offensive rebound and scored with 1:22 to play to bring Davidson within a point.
Ellington then hit his jump shot from the right wing for a 66-63 lead and, after Davidson missed a field goal attempt, Ty Lawson made two free throws to give the Tar Heels a five-point cushion with 30 seconds remaining.
Davidson (1-1) was led by Lovedale with 12 points.
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