Bobrovsky beat the Devils for the third time this season by withstanding a late flurry in the final minutes moments before and after New Jersey pulled goaltender Keith Kinkaid for the extra attacker.
Columbus' Boone Jenner scored in the first period and defenseman Scott Harrington netted the tiebreaking tally in the second.
Taylor Hall scored his 25th goal for the Devils, who were unable to match a season high with a fifth straight win. Hall registered a point in his 19th consecutive game.
Kinkaid made 17 saves for the Devils, who were unable to surpass their point total from last season, when they finished with 70 points.
Columbus gained a 1-0 lead 5:10 into the game when Jenner forced a turnover by Ben Lovejoy near the blue line. Zach Werenski's initial shot went off the left post, but Jenner swooped in and tapped in the rebound into the vacated side of the net after Kinkaid was out of position.
The Devils tied it 94 seconds into the second period when Hall completed an end-to-end rush by putting a wrist shot from near the right circle past Bobrovsky.
Columbus regained the lead with 6:50 left in the middle period by catching the Devils on a slow line change.
Artemi Panarin sped into the offensive zone and whipped a cross-ice pass to Harrington, who lifted a slap shot past Kinkaid's left glove and snapped a 21-game goalless drought.
Bobrovsky made Harrington's second goal of the season stand up by making nine saves in the third period.
He made a point-blank stop on Brian Boyle with 2:42 remaining, a sprawling stop on Travis Zajac's attempt during a goalmouth scramble with 2:14 left and then stopped Will Butcher's long wrist shot despite being screened from clearly seeing the puck.
--Field Level Media