Gibson, who missed the previous three games with a lower-body injury, has allowed two goals or fewer in eight consecutive starts (6-1-1).
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Rickard Rakell and Cam Fowler each had a goal and an assist, and Andrew Cogliano and Josh Manson scored for the Ducks, who won for the first time in three games (1-1-1) and extended their home point streak to seven (5-0-2).
Anaheim (32-21-12) holds the second wild card into the Stanley Cup Playoffs from the Western Conference, one point ahead of the Colorado Avalanche, who briefly held the final postseason spot after a 7-1 win against the Minnesota Wild.
"We've had a good rhythm lately," Cogliano said. "That's been a big part of our game."
Zach Werenski had a goal and an assist, Oliver Bjorkstrand had two assists, and Sergei Bobrovsky made 31 saves for Columbus (32-28-5), which is tied with the Carolina Hurricanes for the second wild card in the Eastern Conference.
"It's that time of the year where every team is going 100 percent, playing physical," Milano said. "We've just got to expect it at this point."
Cogliano gave the Ducks a 2-1 lead with a shorthanded goal at 11:17 of the second period.
Manson was in the penalty box for interference on Seth Jones when Blue Jackets forward Artemi Panarin was unable to stop the puck on a pass back to him at the Columbus blue line. Cogliano retrieved the puck and beat Bobrovsky between his pads on a breakaway for the 18th shorthanded goal of his NHL career.