The Jets snapped a three-game losing skid with the win.
Jets defenceman Carl Dahlstrom appeared to have broken the scoreless drought 8:27 into the third, but the goal was called back due to the play being offside.
There was no scoring in regulation and the game went to overtime.
Connor Hellebuyck stopped all 28 shots for Winnipeg, posting his 14th career shutout in the process as Winnipeg moved to 5-5-0 on the season.
Mike Smith turned aside 23 shots for Edmonton, who saw their two-game winning streak come to an end.
Oiler winger James Neal said the goaltending was strong on both sides.
"They (Smith and Hellebuyck) were great. They were really good. High-end saves back and forth. I think I just heard Smitty say it was not too much fun for the goalies, but I think it's obviously fun to watch," he said.
Winnipeg captain Blake Wheeler said it was good to get the win following some challenging times.
"It’s good to get a result. Obviously, it’s been tough around here. I think the quality of our play isn’t reflective of of the results we’re getting recently. So, it’s good to finally get one," he said.
Winnipeg Jets Head Coach Paul Maurice posted his 700th career win on the night, becoming only the 7th coach in NHL history to do so.
"No, when you’re starting young you’re thinking ‘Wow, if I could coach 500 games in this league that would be a milestone.’ You don’t even consider coaching 1,000 games. It’s really since I’ve been in Winnipeg and come to Winnipeg that the numbers have really started to pile up. The last few years started to coach the best teams I’ve ever coached here so you win more hockey games. It’s nice. I’m still a young man. Would like to do it for a while,” he said.
EDMONTON-Nugent Hopkins (miss), McDavid (miss)
WINNIPEG-Connor (score), Laine (score)
SHOTS-EDMONTON 28 WINNIPEG 23