The Blues scored three times in the first 9:45 to jump in front 3-0 and chase Nashville goalie Pekka Rinne.
Jaroslav Halak made 28 saves for the Blues and improved to 9-3-3 against the Predators.
Backes, Vladimir Sobotka, T.J. Oshie and Alex Steen scored for St. Louis, which was 2 of 4 on the power play.
St. Louis has won four of its past five home openers.
Nashville, which missed the playoffs last season, is 7-7-1 in season openers.