Edmonton scored three times in each of the first two periods to win for just the second time in 11 games.
A home victory by Minnesota over the lowly Oilers would have given the Wild their first post-season spot in five years. Minnesota can still earn a playoff bid by downing Colorado Saturday, but a loss would give Columbus a chance to vault past the Wild into the final playoff position.
Potter scored just 27 seconds into the game and added a goal with 1:22 left in the first period that gave Edmonton a 3-0 led.
Nikolai Khabibulin made 38 saves for the Oilers.