Anderson needed to make just 20 saves while shutting out the Oilers for the third time this season.
"You need a little bit of luck to get some shutouts," Anderson said. "And we're playing really well defensively against this team."
The Avalanche had lost four of five following a six-game winning streak.
Also, they have a 3-2 lead in the season series.
Net-minder Jeff Deslauriers was beaten twice on 41 shots for the Oilers, who have a nine-game road losing streak.