Milan Hejduk notched the winner in the shootout 2, at Pepsi Center.
Hejduk beat Nikolai Khabibulin with a wrister to start the shootout, and Peter Mueller followed with another successful shot, this time inside the right post.
Jordan Eberle missed his shot and Semyon Varlamov stopped Sam Gagner to end the contest.
Cody McLeod and Mueller netted second-period scores for the Avalanche, winners in three of four.
Varlamov ended up with 28 saves.
"It sure was a tough third period. We have to finish harder," Mueller said. "We got great goaltending and D, and they kept us in it until we could come up with the win."
Ryan Smyth and Taylor Hall tallied for the Oilers, who have lost four of five.
Khabibulin finished with 30 stops.
Smyth knocked in a Ryan Nugent-Hopkins rebound to give the Oilers a 1-0 edge just before the first intermission.
McLeod evened the game with 4:44 played in the second period, then Mueller flipped the rebound of a Hejduk chance into an open net just after the midway point for a 2-1 Avs edge.
Edmonton had a potential game-tying goal by Ales Hemsky taken away near the midway point of the third after Sam Gagner was ruled to have made contact with Varlamov in the crease.
"The explanation was that I was in the crease," Gagner lamented. "It's frustrating, but there's nothing I can do."
But Hall eventually tied the game by sweeping in a loose puck from his belly at the right post with 4:43 remaining.
Edmonton won the season series 3-2-1...The Avalanche improved to 17-14-4 at home and the Oilers fell to 10-21-3 on the road...Colorado upped its shootout mark this season to 8-1...Defenseman Andy Sutton committed Edmonton's only two penalties in the contest.