Edmonton's losing streak removed the Oilers from playoff contention, but they finally picked up a victory thanks in large part to a 33-save performance from Devan Dubnyk.
Schultz broke a 1-1 tie with 5:46 to go in the first period and Edmonton expanded its lead in the middle stanza on goals from Ryan Nugent-Hopkins and Jordan Eberle.
Colorado's lone goal came from P.A. Parenteau, his 18th of the season.
Semyon Varlamov gave up all of the Edmonton goals on 24 shots.