Shawn Horcoff also scored twice and added two assists for Edmonton (4-6-0), which won for just the second time in its last eight games.
James Sheppard, Pierre-Marc Bouchard, Brian Rolston and Mark Parrish answered for Minnesota (7-1-2), which lost for the second time in as many nights but has still recorded points in all but one of its games this season.
The Oilers entered Thursday having had nothing but trouble against the Wild in recent history, scoring just twice in its last six meetings with Minnesota. Edmonton equalled that total in the first period alone.
The Oilers got to Minnesota starter Josh Harding just three and a half minutes in, as defenceman Ladislav Smid's wrist shot was tipped into the net by Horcoff.
Edmonton extended its lead midway through the first, after Hemsky picked up a loose puck up in front of the net and snapped his first goal of the season over Harding's shoulder.
After some sustained pressure in the second period, Minnesota cut into the lead on Sheppard's first career NHL goal, knocking his own rebound past Oilers netminder Dwayne Roloson.
Edmonton bounced back less than a minute later, as Horcoff's shot hit Harding, bounced off Wild defender Kim Johnsson and went in. It was only Edmonton's second power-play goal in 38 attempts on the season.
Minnesota drew to within one with five minutes remaining in the period after Nick Schultz's point shot was deflected in front and trickled past Roloson to Bouchard, who sent a backhand shot into the open net.
Rolston evened the score early in the third period, converting an Eric Belanger shot that caromed off defender Tom Gilbert's skates directly to him at the side of the goal.
Edmonton regained the lead five minutes later on a highlight reel goal by Hemsky as he undressed Johnsson and deked out Harding before sliding it through his legs.
Minnesota rallied midway through the period, as Roloson mishandled a glove save on a shot by Parrish and it trickled over the line.
Edmonton travels to L.A. to face the Kings on Saturday while the Wild wrap up a three-game road swing in Colorado on Sunday.
Notes - Edmonton F Sam Gagner played in his ninth game of the season, the maximum he is allowed to spend with the Oilers before the first year of his contract kicks in. Considering that the team told him to move from his hotel room into a more permanent residence, it would appear he is staying. ... Hemsky's first-period goal was his 200th NHL point. ... Pavol Demitra (groin) missed his second game in a row. He has three goals and five assists in eight games. ... Wild G Niklas Backstrom, who did not get the start, has been an Oiler killer throughout his career with three shutouts and five wins in five meetings. Harding's only previous start against the Oilers was a shutout win.