The Blue Jackets scored three times in the second stanza with Jack Skille adding to the tally. Columbus built a 4-0 lead heading into the third and held on to reach 10 wins for the season.
Columbus gained revenge for a 7-0 battering at the hands of Edmonton earlier this month.
Sergei Bobrovky earned the victory by making 25 saves. He cooled off the Oilers, who had won four of their previous five games.
Ilya Bryzgalov allowed four goals on 23 shots before being replaced by Devan Dubnyk to start the third period.