Gustavsson stood up to a Blue Jackets barrage in the first period, turning aside all 18 Columbus shots as Detroit grabbed a 1-0 lead on Daniel Alfredsson's first tally as a Red Wing.
After Cam Atkinson dented Gustavsson for a power-play equalizer in the second period, Detroit's Todd Bertuzzi struck less than 4 minutes later with the eventual game-winner.
Henrik Zetterberg assisted on both tallies for Detroit, which reeled off a third straight win.
Sergei Bobrovsky made 30 saves for the Blue Jackets.
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