Charlie Coyle, Mikael Granlund and Zach Parise also scored for the Wild (24-16-3), who have gone 2-0-1 in their last three games after losing five of their previous six. Minnesota remains in sixth place in the Western Conference playoff race.
Nail Yakupov, Magnus Paajarvi and Shawn Horcoff responded for the Oilers (16-19-7), whose slim playoff hopes took another hit. Edmonton has lost six in a row on the heels of a five-game winning streak.
Once again, the Oilers found themselves behind early as the Wild scored just over a minute into the game. Brodziak sent a knuckler of a shot on Edmonton starter Devan Dubnyk and was able to get in front to knock home his own rebound for the 1-0 Wild lead.
Edmonton tied the game with 15 minutes gone in the opening period as Taylor Hall's shot got caught up in the equipment of Wild defender Brett Clark before falling in front of the net where Yakupov was able to swoop in and score the 11th goal of his rookie campaign on Minnesota goalie Niklas Backstrom.
The Wild regained their one-goal edge three minutes into the second period as a point shot from Stoner clipped Coyle in front and caromed past a screened Dubnyk to make it 2-1.
Minnesota went up 3-1 three-and-a-half minutes later as a rebound off of the boars was tipped out front to Granlund who slammed it into a wide-open net with Dubnyk going the other way.
It took just 20 seconds in the third for the Wild to go up 4-1 on a power-play goal. Parise slid a puck through the crease and went behind the net untouched and still had time to backhand home his initial shot for his 16th of the season.
The Wild went up 5-1 five minutes into the third as Jason Pominville sent Brodziak in on a breakaway. Brodziak actually hit the post on his shot, but Dubnyk put it into his own net with his backward momentum.
Edmonton got a goal back at the 10-minute mark as Hall was able to sneak a pass through the crease to Horcoff, who was stationed in front and tapped home his seventh.
The Oilers made it a bit more interesting less than three minutes later as Yakupov dipsy-doodled through traffic before ringing a shot off the post. Paajarvi swooped in to hammer home the rebound past Backstrom to make it 5-3.
The Wild conclude a three-game road trip in San Jose on Thursday. The Oilers are off until Friday when they travel to Colorado to take on the Avalanche.
Notes: It was the third of four meetings between the two teams this season, with the Wild having won both previous encounters. Minnesota has had a great deal of success against the Oilers in recent years, coming into the game having won three straight and 13 of the last 16 encounters. Minnesota had also won six of its past seven in Edmonton… It was the first game for the Oilers since Monday’s announcement that GM Steve Tambellini had been sacked, with former head coach Craig MacTavish coming in as his replacement… Edmonton called up forwards Anton Lander and Teemu Hartikainen from Oklahoma City and inserted both players into the lineup. Ryan Jones and Jarret Smithson came out… It was the eighth of nine sets of games on back-to-back nights for the Wild this season. The Wild entered the contest 4-3 in games on the second straight night… Some good news out of Minnesota as goalie Josh Harding was sent to the Houston Aeros of the AHL on a conditioning assignment. Harding has been on injured reserve since Feb. 12 as he has received treatment for multiple sclerosis… Notable absences from the Wild lineup included forward Dany Heatley (shoulder surgery) and centre Zenon Konopka (foot injury)… Out for the Oilers were Ales Hemsky (broken foot) and Eric Belanger (groin).