More importantly, Oilers forward Ethan Moreau was fine after taking a skate to the face early in the third period. Morneau was cut above the right eye by Marian Gaborik's skate. He returned to the bench after being patched up.
Edmonton was fortunate to emerge from the second period with a 2-1 lead despite being outshot 21-4 in the period and 31-11 through 40 minutes.
"It was fitting to win a game like that when we have lost so many where we have out-shot the opposition over the years, particularly against Minnesota," Oilers coach Craig MacTavish said. "There have been lots of nights in here where we have nailed them with a lot of shots and lost the game. It's the old adage: What comes around, goes around."
"Sometimes when you have a young team, you can get panicking a little bit in your zone," Garon said. "We were giving up a lot of shots, but at the same time most of the shots were coming from the side and they were shooting from everywhere. Sometimes the shot clock doesn't really reflect the game."
"We talked about shooting high, he was covering low very good," Gaborik said of Garon. "A lot of shots we had on him were very low shots. In that second period, we could have scored four goals easily. It could have been a totally different game."
After spending the majority of the second period on the defensive, the Oilers put the game away with two goals early in the third -- both from Brodziak.
With the Oilers up 2-1, the third-year forward extended the lead two minutes into the period, picking up his own rebound and chipping it over the glove of Josh Harding.
Brodziak gave the Oilers a 4-1 advantage 2:21 later, picking up another rebound at the left hash mark and firing a shot into the top corner for his eighth of the season. It was his first career two-goal game.
"It feels really good to have a game like this," Brodziak said. "For a while, I've been struggling personally and haven't been able to put my chances in the back of the net. Tonight when I got the chances I made sure I was bearing down on them and I put them in the right spots I guess. It feels good to be able to contribute like that."
Harding allowed two goals on 12 shots in the third after relieving starter Nicklas Backstrom, who surrendered two goals on 11 shots through 40 minutes.
"I could see that [Backstrom] was a little nervous or out of position a little bit," Wild head coach Jacques Lemaire said. "That's why at the end of the [second] we decided to give him a chance to recover from it."
Edmonton opened the scoring with 1:48 in the first period. Andrew Cogliano made a cross-ice pass to Pisani, whose wrist shot eluded Backstrom's glove.
The Wild tied it eight minutes into the second period as Demitra picked up Kurtis Foster's point shot rebound at the side of the net and tucked it under Garon.
Edmonton restored its one-goal advantage 2 1/2 minutes later on the power play as Stoll unleashed a shot from the point which eluded a screened Backstrom.
The Oilers were fortunate to emerge from the second period with a 2-1 lead after being outshot 21-4 in the period and 31-11 through 40 minutes.
Already without forwards Shawn Horcoff and Raffi Torres for the remainder of the season, the Oilers announced Tuesday that Sheldon Souray will also not be able to return this season. The defenseman, who signed a $27-million, five-year contract in the offseason, had arthroscopic surgery on his left shoulder late last week. In 26 games, Souray had three goals and 10 points. ... Wild defenseman Kim Johnsson missed the game due to illness ... With Harding coming in to take the loss, Backstrom still has yet to lose to the Oilers. In his eight previous career starts against Edmonton, Backstrom was 8-0-0 with a 1.30 goals-against average, .947 save percentage and three shutouts. ... Newly acquired forward Curtis Glencross assisted on both of Brodziak's goals.
Information from The Associated Press contributed to this story.