With just 4:38 remaining in regulation, Stoll picked up a blocked Marc-Andre Bergeron shot in the slot and out-fought Keith Carney for the puck before picking the upper right hand corner on Wild starter Manny Fernandez to give the Oilers a 2-1 lead.
Edmonton took the game outright 14 seconds later as Shawn Horcoff stole the puck in the Minnesota zone and undressed Petteri Nummelin before putting a backhand past Fernandez to give the Oilers the 3-1 win.
With the win, the Oilers retained top spot in the Northwest over the Wild. Edmonton is now 17-12-2 on the year with the Wild closely trailing at 16-13-2.
The Wild opened the scoring, connecting on their first shot of the game. Todd White looked like he might pass, but snuck a wrist shot stick-side on Edmonton starter Dwayne Roloson to put the Wild up 1-0 just under four minutes in.
The Oilers had a great chance to even the score with eight minutes gone in the second and a two-man advantage for 1:40, but Fernandez and the Minnesota penalty killers kept Edmonton from coming close.
Edmonton almost knotted the game short-handed as Marty Reasoner and Shawn Horcoff went in on a two-on-one late in the second period, only to have Horcoff's shot hit Fernandez in the leg and drift just over the top of the Minnesota net. The game remained 1-0 after the second.
Edmonton would finally pull even with three and a half minutes played in the third as defenceman Matt Greene scored his first ever NHL goal. Greene put a deke on Fernandez and scored on a backhand to set up the Oilers' comeback.
The Oilers return to the ice on Friday with a quick trip to Colorado. Minnesota wraps up a three game western road swing in Vancouver on Saturday.
Notes Thursday's match was just the first of eight meetings between the Oilers and Wild this year. Last season Minnesota was a commanding 6-2 in the series and won all four games in Edmonton. . . . Assistant captain Wes Walz returned to the Wild lineup for the first time after missing the last 10 games with a hip injury. . . . Even on separate teams the goaltender debate between Dwayne Roloson and Manny Fernandez continues. Going into the match with a 2.40 goals-against average and .920 save percentage, Roloson had statistically outperformed his former teammate and current Wild starter Fernandez to this point in the season. Fernandez has a 2.81 GAA and .907 save percentage.