Isac Lundestrom tied it 1-1 on a breakaway at 10:23 of the first, scoring on the backhand through Merzlikins' pads.
"The one good thing that's happened, it's been rare where we've had more than two guys having an off night," Ducks coach Dallas Eakins said. "Tonight, we had seven or eight. When that's happening, that puts a lot of pressure on our goaltender. But thankfully we have a world-class one in [Gibson]. That was just an unbelievable performance.
"Columbus did a [heck] of a job. They threw everything to the top of the paint. They just kept coming and coming and coming, but he was outstanding."
Blue Jackets defenseman Zach Werenski had a goal overturned 52 seconds into second period after the Ducks challenged for offside.
Each goalie made one save in overtime.
"We deserved to win that game. That was our game," Werenski told Bally Sports Ohio. "… If we go even longer in overtime, we probably win that game."
Texier, who missed the net on his shootout attempt, said he realized when he shot that his stick was broken.
"I couldn't shoot, but I didn't know [that it was broken]," he said. "That's how it is. You have to know that before."
NOTES:Blue Jackets defenseman Adam Boqvist sustained an upper-body injury and ended his last shift at 3:31 of the second period. There was no update. … Eric Robinson has four scored points (goal, three assists) in a four-game point streak. … Werenski had four shots in a game-high 30:33. … Ducks forward Sonny Milano was held without a shot and played 16:52 in his first game against the Blue Jackets since they traded him to Anaheim on Feb. 24, 2020. He scored 42 points (20 goals, 22 assists) in 116 games for Columbus from 2015-20.