With the Blue Jackets on a two-man advantage, Sergei Fedorov tied the score 4-4 with his second goal of the game with only 23 seconds left in regulation. Jason Chimera also scored for Columbus.
Patrice Bergeron extended his point streak to nine games with a goal and an assist for Boston, which had its three-game winning streak snapped.
Brad Boyes, Wayne Primeau and Stanislav Chistov also scored for the Bruins, who tried to hang onto their lead behind 19 third-period saves by Tim Thomas. Mark Mowers added two assists.
Fedorov tied it with a one-timed slap shot from the right circle on a pass from Vyborny.
Vyborny won it with his ninth goal - on a breakaway - while the Bruins were caught making a line change.
With the score tied 2-2 entering the second period, Boston gained the momentum behind four power plays and jumped ahead with two goals.
Working off the left half boards, Brad Stuart zipped a centring pass to Chistov, who tipped the puck between the legs of goalie Fredrik Norrena to make it 3-2 at 7:49.
Skating on a two-man advantage three minutes later, an open Bergeron curled from the left post and snapped a low shot past Norrena to give the Bruins a two-goal lead with his 12th.
The Blue Jackets found a spark late in the period thanks to Vyborny.
He took a centring pass from Aaron Johnson with his back to the goal, faked inside, spun to the outside and beat a sprawling Thomas with a backhand shot to pull Columbus within a goal.