Mark Scheifele had a goal and two assists for Winnipeg. Kyle Connor, Mason Appleton, Nikolaj Ehlers and Mathieu Perreault also scored.
Winnipeg coach Paul Maurice didn't get much pleasure out of the win.
''That's a perfect example of why coach's years and dog years are the same, the lives lost on the bench tonight between (Edmonton head coach) Dave Tippett and myself,'' Maurice said. ''It was not a particularly well-played game, we can all agree on that, except the skill level in parts of that was extreme.
''If you had fans in the building, that was a roller-coaster for everybody. So we'll feel we gave up way too much, but there's a section when you play Edmonton that they take from you, that they generate that is just so good.
''Aside from that, there was still a big chunk of the game that was loose and ugly and really fun to watch unless you'd like to live a long life as a coach.''
Alex Chiasson and Ryan Nugent-Hopkins had two goals apiece and Kailer Yamamoto also scored for Edmonton, which lost for the first time in four games. Goalie Mike Smith surrendered four goals on 11 shots before being replaced by Mikko Koskinen.
Wheeler's fifth goal of the season at 6:22 of the third put Winnipeg ahead after Edmonton had rallied from a 4-1 deficit and tied the game at 5-all.
Edmonton coach Dave Tippett said his team didn't hit a lull after expending a lot of energy to make it 5-5.
''I don't know if it was so much a lull as much as a mistake that we made,'' he said. ''We turned the puck over at the defensive blue line when it should've come out and then we didn't defend very well in front of the net.
''It wasn't a lull, we made two mistakes and it was in the back of our net.''
Winnipeg goalie Connor Helleybuck improved to 9-1-1 in his last 11 starts versus Edmonton, which had a 45-24 edge in shots on goal. Hellebuyck made a big play on Oilers captain Connor McDavid with a minute to play and the goaltender on the bench.
The Jets earned the victory after dropping a 2-1 decision to the Ottawa Senators on Saturday night.
Winnipeg improved to 2-1 against Edmonton this season. The two teams meet again Wednesday night.
The Jets and Oilers complete a two-game set in Edmonton on Wednesday night.
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