The Blue Jackets extended their club-record winning streak to eight games.
MacKenzie tied the game with 8:36 to go in the second period and Columbus went in front for good when Matt Calvert scored on the power play five minutes later.
Bobrovsky, who has been in goal for the last five games of the winning streak, made 26 saves.
The five Columbus goals were all scored against Ray Emery, who stopped 34 shots.
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