Devin Setoguchi also scored for Minnesota (8-6-2), which has won two straight. Niklas Backstrom made 25 saves in the victory.
Ryan Smyth had the lone goal for the Oilers (6-7-3), who have lost three of the first four in a five-game homestand that will lead into a nine-game road trip. Devan Dubnyk stopped 25 shots in defeat.
With 2:33 left in the game, Edmonton's Taylor Hall hit Minnesota's Cal Clutterbuck knee-on-knee at center ice. Hall was given a major penalty for kneeing and was ejected.
The play could also lead to supplemental discipline for Hall once the NHL reviews it.
Clutterbuck stayed on the ice, writhing in pain, before he was helped to the dressing room.
Minnesota took a 2-1 lead just over two minutes into the third period when Cullen sent a pass in front to a streaking Setoguchi, who beat Dubnyk with a quick shot.
Edmonton had a chance to tie it midway through the period on a breakaway, but Sam Gagner sent a shot wide.
Cullen then gave his team a two-goal cushion with 6 minutes left when he chose to shoot on a 2-on-1 break and sent a high drive past Dubnyk.
The Oilers' best chance in the first half of the game came six minutes into the second when Nail Yakupov fed Gagner on a 2-on-1 with Gagner, but Backstrom came across to make the save.
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Minnesota came close midway through the second with a flurry in front that included a huge save from Dubnyk in tight on a rebound from Dany Heatley, and another drive off the post.
Edmonton broke the scoreless deadlock 12:26 into the second when Smyth picked up a rebound behind the net and quickly looped around to put the puck in from the other side before Backstrom could get across.
It was the second goal of the season for Smyth, who celebrated his 37th birthday on Thursday.
The Wild tied it with five minutes to play in the period as Cullen outmuscled Mark Fistric to the puck and then beat Dubnyk with a backhanded shot through the legs.
NOTES: It was the first of four games this season between the teams. Last season, the Wild won four of six after a six-game sweep in 2010-11. The Wild entered with a 27-8-2 record against the Oilers over the last six seasons. ... Oilers D Theo Peckham played in his first game of the season. Veteran D Ryan Whitney was a healthy scratch for the fourth time this year. ... Backstrom played after recovering from a bout with the flu. He improved to 23-3-1 against Edmonton. ... Oilers forward Ryan Jones (eye) had been cleared for contact and could be back in the lineup on Saturday. Forwards Anton Lander (foot) and Shawn Horcoff (hand) are week-to-week.
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