The Eagles held Duke to a season-low 63 points and had a four-point lead with under eight minutes to play, but converted just one of their final eight field goal attempts.
Thanks to a pair of Jared Hamilton free throws with 17.2 seconds remaining, the Eagles defeated UNC for the first time since February 2010.
Steffon Mitchell took just four shots but impacted the game in a plethora of ways, while Julian Rishwain and CJ Felder stepped up for a combined 21 points off the bench.
The Eagles forced 17 turnovers and Jay Heath, Derryck Thornton, and Nik Popovic all scored in double figures in a season-opening 77-70 win against Wake Forest.
The likes of Derryck Thornton, Steffon Mitchell, and Jared Hamilton will aim to provide BC leadership alongside a group of freshmen brimming with potential.