Perreault opened the scoring when he beat Pekka Rinne with a wrist shot at 6:41 of the first period. Wilson tied it in the period with a snap shot that Tomas Vokoun was unable to stop to his glove side.
Wilson has five points in four preseason games.
The Predators made it 2-1 midway through the second period on Halischuk's tip-in.
Weber skated low through the middle to beat Vokoun with 5:23 left in the second.