Sonny Milano and Zach Werenski scored for the Blue Jackets, who have lost three in a row on the road. Sergei Bobrovsky stopped 31 shots.
Columbus is tied with Carolina for the second wild card in the East and is seven points behind Pittsburgh for third in the Metropolitan Division.
Cogliano put Anaheim in front 2-1 at 11:16 of the second period with his 15th short-handed goal for the Ducks, one shy of Paul Kariya's team record. Artemi Panarin could not collect a pass by Pierre-Luc Dubois from the neutral zone back into the Columbus end while under pressure from Cogliano, giving the Ducks' forward a breakaway and he beat Bobrovsky between his legs.