Josh Woodrum was 25 of 32 for 239 yards passing and added 44 yards rushing for the Flames (3-2), who finished with 263 rushing yards on 50 carries.
Two of Rice's three scores came in the first half, helping Liberty to a 21-14 lead at the break. A Josh Lunsford 28-yard field goal with 5:19 remaining pushed the Flames lead to two possessions.
George State (1-3) made a final charge however, as a Nick Arbuckle 8-yard run cut the Flames lead to 38-33. After a Liberty field goal, the Panthers had a final chance to tie it but Arbuckle's pass was intercepted.
Arbuckle led Georgia State with 394 yards passing and three touchdowns.