Edmonton overtook Winnipeg for second place in the North Division by a single point with 58.
Leon Draisaitl had a goal and an assist for the Oilers.
Alex Chiasson also scored for Edmonton.
Mike Smith made 29 saves for the Oilers (28-16-3).
Mark Scheifele scored for the Jets.
Connor Hellebuyck and Laurent Brossoit combined to make 19 saves for Winnipeg, who dropped to 27-18-3.
Alex Chiasson got the Oilers on the board 16:22 into the first when he converted an Adam Larsson feed past Connor Hellebuyck, beating him with a low shot.
The goal was his 8th of the season.
Connor McDavid made it 2-0 at 18:31 off of a turnover.
Pierre-Luc Dubois left a drop pass for Blake Wheeler as he gained the Edmonton blue line which Wheeler overskated.
Tyson Barrie tipped the disc over to McDavid, who skated into the Winnipeg end with the puck before hitting Barrie in the high slot with a pass with the Oiler defenceman promptly getting a shot off which Hellebuyck stopped and McDavid knocked the rebound past him.
Connor McDavid gave Edmonton a three-goal cushion 3:35 into the second when Dominik Kahun hit him with a stretch pass, sending the NHL's leading scorer on a partial breakaway.
McDavid moved in and faked a slap shot before beating Hellebuyck between the legs with a wrister to score his 27th goal of the season.
A bad pinch by Derek Forbort put the Jets down 4-0 11:40 into the second.
The Winnipeg defenceman got caught deep in the Oiler zone when Ryan Nugent-Hopkins poked the disc past him, giving Nugent-Hopkins a 2-on-1 with Leon Draisaitl.
Nugent-Hopkins hit him with a crisp pass which Draisatl hammered past Hellebuyck from his off wing to score his 23rd goal of the season.
Darnell Nurse made it 5-0 13:18 into the second when he converted a Jesse Puljujarvi feed past Hellebuyck, beating him between the legs.
The goal was his 15th of the season.
Mark Scheifele got Winnipeg on the board at 15:06 when he fired a Paul Stastny pass past Mike Smith to make it 5-1.
The goal was his 19th of the season.
McDavid scored on a breakaway with 3:30 left in the second period to complete the hat-trick.
The goal was his 28th of the season.
Laurent Brossoit started the third period in goal for Winnipeg.
There was no scoring in the third period.
The same two clubs face each other again Wednesday night in Winnipeg.
SHOTS-EDMONTON 25 WINNIPEG 30