Kelly, who had missed 13 games with a right foot injury, canned 10-of-14 field goal attempts -- including 7-of-9 from 3-point range -- as the Blue Devils (25-4, 12-4 ACC) turned back a late Miami charge.
The Hurricanes trailed 77-70 with 1 1/2 minutes left but rallied down the stretch to make it close. A desperation 3-point try by Rion Brown, however, rimmed out at the final buzzer.
Quinn Cook chipped in with 15 points in Duke's win.
Shane Larkin scored 19 of his 25 points in the second half for Miami (23-5, 14-2), which was denied a chance to clinch its first-ever outright ACC regular-season title.
Kenny Kadji added 17 points and 10 rebounds in the loss.
2014: The Year in Music [PHOTOS]