Woodrum completed 15 of 22 passes for 214 yards for the Flames (6-3, 2-0 Big South). D.J. Abnar ran for 83 yards and a touchdown.
Woodrum's 2-yard touchdown run early in the first put the Flames up 7-0. He followed up in the second quarter with a pair of scoring passes - a 29-yard play to Gabe Henderson and a 70-yarder to Darrin Peterson - to give Liberty a 21-0 halftime advantage.
Presbyterian's only score came early in the fourth on a 5-yard run by Jordan Hallums and the Flames led 21-7.
With just over a minute to play, Abnar took it in from a yard out to put the game away.
Heys McMath finished with 18-of-31 passing and 170 yards for the Blue Hose (5-4, 2-2). He was intercepted four times.