Kelly hit eight free throws in the home stretch when the Blue Devils (13-2, 1-0 ACC) finally pulled away from Tech (7-8, 0-1).
Duke was 29-of-36 from the free-throw line. Georgia Tech was 12-of-19 and had two starters with five fouls apiece.
Seth Curry added 15 points for Duke, who lost their first game of the season at Temple Wednesday. Quinn Cook had 10 points.
Glen Rice led Georgia Tech with a career-high 28 points and eight rebounds. Mfon Udofia scored 19 points, but it was not enough to prevent the Yellow Jackets from dropping their fourth consecutive game.