Adama Adams added 16 points while Shaquille Mitchell and Matthew Hezekiah chipped in 10 apiece for the Bulldogs.
The game saw its seventh tie, 59-59, after Toombs converted two free throws with 4:44 left to play. Toombs knocked down a 3-pointer a minute later to extend South Carolina State's lead to 67-61.
NJIT (1-2) cut the deficit to two, 76-74, with 26 seconds left but Toombs made his ninth free throw of the night and PJ Miller missed a desperation 3-pointer as time expired.
South Carolina State (3-1) was without starters Devin Joint and Randall Black, both of whom are sidelined with torn knee cartilage.
Ryan Woods led NJIT with 20 points.