Wheeler and Patrik Laine also scored for the Jets (37-28-6), who have won four in a row to move into a wild-card spot in the Western Conference.
Connor Hellebuyck made 36 saves to collect the win in the Winnipeg net.
“He’s been our best player all year and it showed again tonight,” Connor said. “He was outstanding, he never waivered in confidence.”
The Jets are 11-5-1 in their past 17 games.
Tyler Ennis and Connor McDavid scored for the Oilers (37-24-9), who have lost two straight.
“That’s karma,” McDavid said. “We have had a couple of games where we have gotten points where we probably didn’t deserve points. Tonight, I thought our game was pretty good and we don’t get any points. That is the way it goes.”
There was no scoring in the first period, with Oilers goalie Mike Smith making 11 saves, while Hellebuyck stopped nine in the Winnipeg net.
The Oilers broke the deadlock nine seconds into the second when Hellebuyck bobbled the puck behind the net and Kailer Yamamoto directed it in front to Ennis, who was able to nudge it into a wide-open net.
Winnipeg tied the game midway through the first as a Wheeler pass was inadvertently swatted into the net by Oilers forward James Neal as he tried to break up the play, going down as Wheeler’s 22nd.
A few minutes later, Jets defenceman Neal Pionk saved a sure goal, swatting a puck out of mid-air to safety just before it could cross the goal-line.
It was Smith’s turn to cough up a puck behind the net with three-and-a-half minutes to play in the middle frame, as Eakin was able to send it in front to Laine for his 28th.
Edmonton knotted the game back up with 1:37 left in the second as McDavid, who returned from missing the last game with an illness, made a terrific deke in tight to record his 34th goal.
Winnipeg made it 3-2 just 29 seconds into the third as Connor was sent in alone and made no mistake in scoring his 37th goal and 200th career NHL point.
After a frantic final couple minutes with Smith on the bench and the Oilers all over the Jets net, Connor put the game away with an empty-netter.
The Oilers were scheduled to close out a four-game homestand against the New York Islanders on Friday, while the Jets are expected to be in Calgary against the Flames on Saturday.
Notes: Jets head coach Paul Maurice recorded his 1,600th NHL game behind the bench, becoming just the fifth head coach in league history to reach the mark, joining Scotty Bowman (2,141), Joel Quenneville (1,705), Barry Trotz (1,673), and Al Arbour (1,607).
This report by The Canadian Press was first published March 11, 2020.
Shane Jones, The Canadian Press