Torrey Craig added 15 points and eight rebounds and Jodd Maxey scored 13 and grabbed nine boards to help SC Upstate (6-7) win its 12th straight home game, dating back to last season.
After the game was tied 38-all with 13:43 remaining, SC Upstate closed out Hampton with a 30-11 run. Greene and Craig sparked the run with consecutive 3-pointers.
The Spartans held the Pirates (2-10) to 31 percent (9 of 29) shooting in the second half.
Ricardo Glenn led SC Upstate with 11 rebounds as the Spartans outrebounded Hampton 46-32.
Ahead 28-25 with 1:23 left in the first half, Craig hit back-to-back 3-pointers, including one at the buzzer for a 34-25 Upstate lead at halftime.
Du’Vaughn Maxwell finished with 17 points and 10 rebounds for the Pirates.