Bobrovsky turned aside all 39 shots he faced in regulation and overtime and added another on Oliver Ekman-Larsson's shot in the tiebreaker to secure the victory.
Artem Anisimov and Mark Letestu, meanwhile, tallied against the Coyotes' Mike Smith in the shootout as the Blue Jackets recorded their fourth straight win -- all via the post-regulation tiebreaker.
The decision gave them at least one point in 10 consecutive games (6-0-4), a franchise record.
Smith finished with 23 saves as Phoenix was blanked in a second straight contest.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys