The Eagles face in-state rival N.C. A&T on Thursday with a chance to complete an undefeated season in the Mid-Eastern Conference.
North Carolina Central (23-6, 15-0) went on a 13-2 run early - including back-to-back 3-pointers by Anthony McDonald - and had a six-point spurt a little later to lead 33-25 at the break.
An 11-2 run at the start of the second half, including another 3 by McDonald, pushed the lead to 44-27. Another 11-point spurt a few moments later made it a 20-point game.
Savannah State responded with a nine-point run - capped by Alante Fenner's 3-pointer - to cut the deficit to 11 at 54-43 with 4:51 left, but the Tigers only made two more baskets down the stretch.
Savannah State (9-20, 5-10) was led by Fenner with 11 points.