Glenn also pulled in 11 rebounds and Torrey Craig logged 15 points for the Spartans.
USC Upstate (11-10, 4-4 Atlantic Sun) never trailed in the game and started the second half with a 36-25 lead over North Florida.
North Florida (11-11, 5-4) fell behind 49-30 on a Greene basket from beyond the arc at 16:27 of the second period. It was the Spartans largest lead of the game and proved too much for the Ospreys to overcome down the stretch.
Dallas Moore led North Florida with 18 points while the Ospreys shot only 33 percent from the field. The Ospreys committed 18 turnovers while the Spartans had just 10. Travis Wallace, North Florida's leading scorer was limited to just four points.