Edmonton ended a four-game losing streak, but the Wild saw its skid reach six games. Despite the slump, Minnesota still has a one-point lead over defending Western Conference champion Vancouver at the top of the Northwest Division.
The Oilers scored the game's first four goals and Eberle started things by coming through on the power play with 4:03 left in the opening period. After Ryan Smyth added a first-period goal, Lennart Petrell and Eberle scored in the second.
Eberle has 15 goals for the season.
Nikolai Khabibulin had his shutout bid snuffed out by Dany Heatley 7:57 into the third. Khabibulin made 30 saves.
Niklas Backstrom stopped 27-of-31 shots for the Wild.