The Spartans have won four straight games and trail MEAC leader Hampton by just one-half game in the conference standings.
D'Shon Taylor and Jonathan Wade each finished with 14 points and Jeff Short added 13 for Norfolk State (10-12, 6-1), which tied a season-best with 14 made 3-pointers.
The Spartans opened on a 15-4 run and led 40-24 at the break. Jordan Butler hit a pair of free throws with 16:51 left which pushed Norfolk State's lead to the 20-point plateau, and Oliver's sixth 3-pointer made it 81-49 with 7:05 remaining.
Chris Martin led Savannah State (7-11, 3-4) with 16 points. Dexter McClanahan had 15 points and Troyce Manassa added 14 for the Tigers.