Corey Potter scored twice in a three-goal first period which sent Niklas Backstrom to the bench, and Edmonton wrecked Minnesota's playoff-clinching party with a 6-1 decision at Xcel Energy Center.
Backstrom was pulled after giving up three goals on five shots in the first 18:38 of regulation, including one to Taylor Hall. Josh Harding fared little better in relief, allowing three more scores on 12 shots for the remainder of the contest.
"It was one of the weirdest games I've ever played in and obviously one of the most disappointing games I've ever been in," said Wild forward Matt Cullen. "We got spanked in a game we absolutely needed to win.
Nail Yakupov also lit the lamp on two occasions for the Oilers, who played spoiler thanks to their second win in the last 11 games.
Jordan Eberle added a goal and two assists to back a 38-save effort by Nikolai Khabibulin.
"He did a great job. It would have been nice to get him a shutout. He was unbelievable," said Oilers forward Sam Gagner of his goaltender.
Mikko Koivu provided the lone offense for the Wild, who simply needed to win in order to gain their first postseason berth since 2008.
Potter opened the scoring just 27 seconds after the opening faceoff, and Hall doubled the Oilers' advantage just over eight minutes in.
It was 3-0 for Edmonton on Potter's second of the period, coming with 1:22 before intermission, and signaled Backstrom's exit.
Eberle beat Harding with 4:09 played in the second period, then Yakupov scored twice in a span of 2:42 to increase the Oilers' edge to 6-0.
Koivu snapped the shutout bid just prior to the midway point of the third period, but the hosts went quietly for the remainder.
"I don't think anyone knows what happened," said Minnesota's Kyle Brodziak. "We're fighting for our lives now."
If Detroit gets a point in its season finale at Dallas, Columbus wins at home against Nashville, and Minnesota loses at Colorado, the Wild will be eliminated.
Despite the setback, Minnesota won two of three in the season series, and hold a 37-13-2 record against Edmonton since the 2005-06 season ... The Wild have not made the playoffs since 2008 ... The Oilers conclude their 2013 slate by hosting Vancouver on Saturday.