Gibson earned the win in relief of Anthony Stolarz, stopping all 18 Blue Jackets shots in the final 40 minutes of regulation. Stolarz left the game following a first period that was all Columbus, stopping 12-of-15 shots.
Cam Fowler, Troy Terry, Trevor Zegras, Adam Henrique and Isac Lundestrom led Anaheim with multi-point nights. Fowler, Zegras, Henrique, Simon Benoit and Max Jones scored.
Mathieu Olivier, Jack Roslovic and Nick Blankbenburg scored for the Blue Jackets, who lost their third straight game and fell to 13-30-2 on the season. Elvis Merzlikins took the loss in net with 28 saves.
As most comeback efforts do, the evening got off to a nightmarish start for the Ducks, who despite a couple of strong shifts early on trailed 2-0 by the first television timeout.
Olivier opened the scoring on an end-to-end rush, taking a bank pass that Eric Robinson chipped around the pinching Fowler, racing ahead on a 2-on-1 and beating Stolarz to the blocker side.
The 25-year-old Olivier has three goals in 40 games this season, matching his NHL career-best set with Nashville two years ago.
Roslovic doubled the advantage four minutes later following a Ducks defensive zone turnover. As Anaheim tried to clear the zone up the left side of the ice, Roslovic stepped in front of a pass at the top of the circle, turning and firing a snap shot just under the crossbar to put Columbus ahead 2-0.
A former Winnipeg Jet, Roslovic has five goals in 10 career matchups against Anaheim.
The Ducks' deficit hit three late in the period on a well-executed offensive zone play by the Jackets. Offseason signee Johnny Gaudreau collected a pass in the right faceoff circle, dancing away from the Ducks defense before delivering a return feed to Patrik Laine, who deftly backhanded it to Blankenburg behind him. Blankenburg took his time to line up his shot, eventually firing it over Stolarz's right shoulder to cap Columbus' three-goal first period.
Blankenburg, a 5-9 defenseman, has points in three of his last five games (1-2=3) and 3-2=5 points in 12 NHL appearances this season.
Gibson replaced Stolarz in net to start the second, and the Ducks seemed to find some life, completely flipping the script on the shaky opening frame.
Seconds after the second period's opening faceoff and as Columbus tried to skate the puck up right wing, Fowler poked it free to the middle of the ice, where Lundestrom turned and lofted an area pass off the far boards to Terry. The All-Star winger sprinted into the loose puck, then directing his pass through a sliding Blue Jackets defender for Henrique to shovel home on the backdoor.