St. Louis improved to 4-0-1 under Ken Hitchcock, who took over the team this month and is off to the best start for a new coach in franchise history.
Backes tallied on a wrist shot to open the scoring 6:04 into the contest and finished things off with an empty-net goal with 1:50 to play.
Chris Porter also scored for St. Louis in the second to put the Blues in front for good and Kris Russell tipped in a shot midway through the third.
The only goal off Jaroslav Halak came with 6:53 left in the first from Mike Santorelli that lifted the Panthers into a 1-1 tie.
Jose Theodore allowed three goals on 30 shots.