Connor Hellebuyck made 37 saves for Winnipeg, which will face the winner of the other North Division series between Toronto and Montreal. The Maple Leafs took a 2-1 series lead over the Canadiens Monday night with a 2-1 victory.
Connor McDavid, Ryan Nugent-Hopkins and Alex Chiasson scored for Edmonton, which hasn't won a playoff series since 2017. Mike Smith stopped 39 shots for the Oilers, who had high hopes for the postseason after finishing second in the North Division, ahead of third-place Winnipeg. Edmonton also won the regular-season series 7-2.
"Everyone put everything they had into it," McDavid said. "Definitely proud of everyone. I thought we were the better team most of the night too. It's just frustrating. But that's the way it goes."
The Jets struck first on a power-play goal by Scheifele at 6:16 of the first period.
Just 1:17 later, McDavid -- the NHL's leading scorer in the regular season -- got his first goal of the series when he scored on a wraparound after a give-and-go with Leon Draisaitl.
The Jets regained the lead off Appleton's deflection of Josh Morrissey's shot at 15:55 of the first.
Nugent-Hopkins tied it again at 3:44 of the second, scoring on a backhander into the top corner.
The Oilers took their first lead of the game at 16:37 of the second on Chiasson's power-play goal. But it was short-lived, as Scheifele connected for his second goal of the night on a slap shot at 6:01 of the third.
The Associated Press contributed to this report.