Julian Gamble had 14 points and Durand Scott and Shane Larkin each had 11 for the Hurricanes (11-3, 2-0 Atlantic Coast Conference).
They led for most of the second half, shot 47 percent on 25-of-53 shooting and held the Tar Heels to one field goal during a critical seven-minute span late.
Miami won its third straight, claimed its first 2-0 start to ACC play since joining the conference in 2003-04 and beat North Carolina for just the third time and first since 2006.
James Michael McAdoo finished with 14 points and Reggie Bullock had 11 for North Carolina (10-5, 0-2), which lost its first two league games for the first time since 2008-09 and fell to 18-3 in the series.
P.J. Hairston hit a 3-pointer with just under 5 minutes left to pull the Tar Heels to 56-55.
But Miami reeled off eight quick points, with Gamble sticking back his own miss before Trey McKinney Jones and Scott hit 3-pointers from the same spot in the left corner. Scott's 3 made it 64-55 with 3:05 to play.
And when North Carolina threatened to claw back in it in the final 90 seconds, Kadji blocked Bullock's layup attempt and a dunk by J.P. Tokoto to essentially seal it.
Kadji reached double figures for the fifth straight game and finished one point shy of the season-high 19 he had last month against Arizona.
This one was tight until the final few minutes, with seven ties and 11 lead changes.
Aside from a span of about a minute in the first half in which the Tar Heels held a six-point lead, neither team led by more than four points until Miami's late surge.
Freshmen Brice Johnson and Marcus Paige had 10 points apiece for North Carolina, which shot just 33 percent (11 of 33) in the second half.
McAdoo, who has scored at least 10 points in all but one game this season, and Bullock combined to take half of the Tar Heels' 60 shots. McAdoo was 5 of 14 while Bullock was 4 of 16.
Both teams were missing key players with injuries. The Tar Heels were without redshirt junior Leslie McDonald, who was held out after tweaking his right knee - the same knee he injured in 2011.
Miami once again didn't have big man Reggie Johnson, a Winston-Salem native who averages a double-double but missed his sixth straight game with a broken left thumb.