Perish completed a career-high 39 of 51 passes for 340 yards, his third consecutive game with at least 300 yards passing.
Indiana State (3-1) scored 21 second-quarter points and took a 24-13 lead into halftime.
A 1-yard touchdown run by Perish with 6:10 to play capped a 9-play, 60-yard drive and gave the Sycamores a 31-13 advantage.
Liberty (3-2) was just 1 of 12 on third and fourth-down conversions combined and was limited to 33 yards rushing.
Gary Owens caught 10 passes for 71 yards and one touchdown for Indiana State.