Cogliano put Anaheim ahead 3-2 at 15:48, beating Hellebuyck from below the right circle for his first goal in 17 games.
General manager Bob Murray said after the game that he has no intention of changing coaches and placed much of the onus for the losing streak on the players rather than on coach Randy Carlyle.
"While it's not my preference to make comments on this topic during the season, our recent play has led to many questions. Our fans are frustrated, rightfully so, and deserve a response from me," Murray said. "At this time, I am not considering a coaching change. I am more focused on our players, specifically with who is going to step up in this situation. The way we played tonight was a step in the right direction, but we need much, much more. We have higher expectations for this group, and they should expect more from themselves."