Chasten was fouled after making a layup with 13 seconds left in overtime and hit the free throw to put the Eagles in front 74-71.
North Carolina Central shot 3 for 6 in overtime, including 2 of 3 from 3-point range.
Bulldogs guard Cario Bennett hit a layup with 11 seconds left to tie the score at 65 and send the game into overtime.
The Eagles (4-3) shot 17 for 26 in the first half (65.4 percent) and led by as many as 18 with 4:52 left before halftime. North Carolina Central led 42-32 at the break.
South Carolina State (3-4) shot 25 of 64 for the game (39.1 percent), including 4 for 25 from behind the arc (16 percent).