Sergei Kostitsyn scored the first goal of the game 3:06 into the first period with a tip-in off of a shot by Weber from high above the right circle.
Ben Eager got the Thrashers even at 15:30 of the second period when he scored with a wrist shot from a few feet in front of the crease.
With Nashville on a power play, Weber gave the Predators a 2-1 lead 11:02 into the third when he blasted a shot from just inside the blue line that went through traffic and past goalie Ondrej Pavelec.
Pavelec and Nashville counterpart Pekka Rinne went the distance in goal. Pavelec stopped 29 shots, and Rinne made 21 saves.
Weber's goal was the first on the power play for Nashville in four preseason games. Nashville goaltender Chet Pickard dressed for his first preseason non-rookie game, but didn't play. This was the first road game of the preseason for the Thrashers.