Singler finished with 24 points and Nelson 23.
Duke played a sluggish first half following its commanding 89-78 victory at third-ranked North Carolina in Chapel Hill Wednesday and found itself trailing 35-28 after Tyrese Rice's two free throws with 4:50 left.
Duke closed to 42-41 when David Thomas sank a layup as time expired.
In the second half, a pair of 17-2 spurts gave Duke an 80-67 lead with 6:03 remaining. Singler buried three-pointers in both runs.
BC (12-10, 3-6) was led by Rice's 28 points and seven assists. Biko Paris scored 11 points and Shamari Spears 10 in the Eagles' sixth straight loss.