Williams and Hawkins each scored 11 in the second half.
Abilene Christian (5-6) extended to 57-51 with 2:17 left on Parker Wentz's 3-pointer and LaDarrien Williams' jumper. Darryl Palmer got SC State (4-9) back within three, but Abilene Christian made 5 of 7 foul shots in the final 30 seconds.
The Wildcats trailed 22-9 in the first half, rallied within seven at the break and opened the second on a 9-0 run to take the lead at 32-30.
Hawkins made a 3-pointer to tie it at 35 and assisted Williams' 3 on the next possession the give Abilene Christian the lead for good.
Edward Stephens scored 14 points and Palmer grabbed 10 rebounds to lead the Bulldogs.