Justin Fontaine and Jason Zucker also scored to help the Wild win for the sixth time in eight games and bounce back after getting shutout on Tuesday.
Jordan Eberle scored his 15th goal for the Oilers, who haven't won on the road in their past six tries.
Edmonton spent most of the second period in the Wild's zone, but didn't generate many shots.
When the Wild got set up on the other end, Prosser's slap shot hit Ben Scrivens' left glove and fluttered in to give Minnesota a 2-1 lead.
It was Prosser's first goal since Feb. 7, 2012, in Columbus.
Fontaine stuffed in a rebound 2 minutes later and Zucker scored 8 seconds into the third on a give-and-go with Dany Heatley.
Scrivens had 29 saves in his Oilers debut after he was acquired Wednesday in a trade from Los Angeles. Scrivens replaces Devan Dubnyk in goal, who played in 32 games for the Oilers and was traded to Nashville for centre Matt Hendricks on Wednesday.
While the Oilers were incorporating new players into their lineup, the Wild carried on without several of their key players.
Zach Parise (foot) and Mikko Koivu (ankle) remain out and top goalie Josh Harding hasn't played the past eight games as he recovers from an adjustment to his multiple sclerosis treatment.
Darcy Kuemper had 20 saves and improved to 3-1 since being recalled from Iowa of the AHL. He's stopped 111 of 116 shots over that span.
Edmonton — the worst defensive team in the NHL — has allowed 28 goals in its past six road games and desperately needs the gritty Hendricks to provide more toughness and Scrivens more consistency in the net.
Scrivens allowed 1.97 goals per game while filling in for the injured Jonathan Quick in Los Angeles, but will probably see that number rise on the defensively challenged Oilers.
NOTES: Scrivens is the fifth goalie to play for the Oilers this season. ... Parise (foot) practiced on Wednesday, but did not give a timetable for his return. ... This was the 1,000th regular season game in Wild franchise history. ... Oilers RW Nail Yakupov left the game with a head injury in the third period. ... Zucker's goal was the fastest to start a period on home ice in franchise history.