The Oilers ended a three-game losing streak, downing the team with the worst record in the NHL.
Ryan Nugent-Hopkins snapped a scoreless tie 7:40 into the second period and Taylor Hall produced the game's key goal by scoring on the power play with 5 seconds left in the middle stanza.
Linus Omark finished the scoring with an empty-net tally.
The shutout was the fourth of Dubnyk's career.
Curtis Stanford gave up two goals on 26 shots. Columbus has lost three straight.