With the win, the Wild leap atop the entire NHL with 33 points and a 15-7-3 record.
Kyle Brodziak netted the game-winner in the 4-3, wristing a shot past goalie Nikolai Khabibulin after Niklas Backstrom stoned Ryan Smyth on the shot prior. Jordan Eberle, Mikko Koivu and Danny Heatley also slotted home goals in the shootout for Minnesota.
The Oilers went up 2-0 on goals by Ryan Nugent-Hopkins and Jordan Eberle, but the Wild cut the deficit to 2-1 when Devin Setoguchi tipped in a shot to the net from Koivu at 11:31 of the second period. Minnesota struck again just three minutes and change later when Brodziak scored on the power play. The third period and overtime were scoreless, paving the way for Brodziak's heroics.
The Wild next welcome the New Jersey Devils -- who have won four of six -- to the Xcel Energy Center on Friday.