Adam Lowry, Nikolaj Ehlers, Pierre-Luc Dubois, Mark Scheifele and Kyle Connor also scored for the Jets, who closed out a 7 game homestand with a win.
Josh Morrissey added a pair of assists.
Connor Hellebuyck stopped 32 shots for Winnipeg, who moved to 9-3-3.
Leon Draisaitl scored a pair of power play markers in the third period to give him a league leading 33 points on the season.
Connor McDavid had a pair of assists.
Mikko Koskinen and Stuart Skinner combined to make 30 saves for Edmonton, who closed out a five game road trip with a loss (11-4-0).
The meeting was the first between the two Canadian clubs since the Oilers were swept by the Jets in last spring's playoffs.
Adam Lowry opened the scoring 2:09 into the contest, stopping Oilers defenceman Duncan Keith at the Winnipeg blue line before breaking in on his off wing and beating Koskinen between the pads with a wrist shot that just trickled over the line.
The goal was his second of the season.
Nikolaj Ehlers scored just under seven minutes into the second when he took a neutral zone cross ice feed from Andrew Copp before unleashing a slap shot that beat Koskinen high glove side.
The goal was his fourth of the season.
Pierre-Luc Dubois redirected a Josh Morrissey shot during a power play to put Winnipeg up 3-0.
Mark Scheifele got hit by Logan Stanley's point shot and the puck went in just inside the far post to give the Jets a commanding 4-0 lead after two periods.
With Edmonton enjoying a two-man advantage Leon Draisaitl got the Oilers on the board 2:32 into the third period, one timing a Connor McDavid feed past Hellebuyck to make it 4-1.
Draisaitl appeared to score again at 3:48 but it was ruled no goal on the ice as Jesse Puljujarvi interfered with Jets goaltender Connor Hellebuyck.
Edmonton Head Coach Dave Tippett challenged the call and the goal was allowed to stand.
The goal was his 9th of the season.
Kyle Connor added an empty netter with 1:37 remaining in regulation to seal the win for the Jets.
The goal extended his 4 game scoring streak.
The two teams meet again Thursday night in Edmonton as Winnipeg kicks off a two-game Western Canadian road trip.
SHOTS-EDMONTON 34 WINNIPEG 35