The Blue Jackets won their fifth in a row and moved two points in front of Detroit for the final playoff position in the Western Conference. The Red Wings lost to Calgary earlier in the evening.
Columbus never led until Tyutin put a wrist shot past Viktor Fasth, who gave up three goals on 27 shots. The Ducks, currently holding down the No. 2 seed in the West, lost their third in a row.
Sami Vatanan scored the only first-period goal to put the Ducks in front, but Blake Comeau tipped in a shot in the second period to tie it.
David Steckel tallied on a slap shot to once again give Anaheim the lead 4:53 into third only to have Columbus come back on a goal from Matt Calvert 5 minutes later.
Sergei Bobrovsky stopped 26 shots to get the win.