Kyle Randall finished with 17 points and four assists for the Spartans (4-16, 4-6 Southern Conference), who went on an 11-0 run midway through the first half to claim a 28-14 lead on a layup by Aaron Brackett.
UNC Greensboro continued its strong play in the second half, pulling ahead by 25 points on Randall's jumper with 18:26 left to play. The Bulldogs (11-11, 3-7) attempted a rally, cutting the lead to 60-54 on a layup by Andy King with 7:51 remaining.
But Samford did not get closer as the Spartans answered with Simpson's two free throws and Randall's 3-pointer. UNC Greensboro added more cushion to its lead by making 17 free throws in the last 2:37 of the game.
John Peterson led Samford with 16 points.