Rackley made 11 of 11 free throws and grabbed eight rebounds, while Felder pulled down nine boards. Dontay Jackson had a career-high seven assists for Jacksonville State (8-9, 1-2 Ohio Valley).
The Gamecocks made 16 of 29 field goals in the first half and took a 41-28 lead into halftime before pushing its lead to 20 with 13:56 to go.
A 3-pointer by Josh Robinson capped a 17-2 Austin Peay (5-9, 0-1) run which made it 54-49 with 6:15 left, but Rackley scored 13 from there — going 8 of 8 from the free throw line in the final 3:33 — to hold off the Governors.
Chris Horton led Austin Peay with 19 points and 13 rebounds.
Jacksonville State, which never trailed, made 19 of 21 free throws.