Backes drew a hooking penalty on the Blue Jackets' Fedor Tyutin 6 minutes into the final frame and capitalized when he one-timed a blind, behind-the-back pass from T.J. Oshie into the net.
It was the first power-play goal of the year for Backes, the team's second-leading scorer, and it improved the resurgent Blues' record to 7-1-2 since Ken Hitchcock was brought in Nov. 6 when Davis Payne was fired following a 6-7-0 start to the season.
Former Blue Jacket Kris Russell notched the equalizer with 8 seconds remaining in the second period and Brian Elliot turned aside 23-of-24 shots for St. Louis.
Derek Dorsett scored and Curtis Sanford made 27 saves for Columbus.
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