Woodrum, who completed 19 of 32 passes for 188 yards, hooked up with Peterson on a 26-yard scoring play midway through the first quarter, and the Flames boosted the lead less than two minutes later when Desmond Rice, 139 yards, rushed for a 23-yard TD.
Rice's score was set up when Delaware State's Esayah Obado was intercepted. Obado, who passed for 227 yards after missing 2014 to injury, was picked off a second time, ending a late Hornets drive at the 1-yard line. He was also tackled in the end zone for a safety.
Liberty's John Lunsford boomed a 52-yard field goal. Lunsford set the school record with a 60-yarder last season.