"It was our mentality the whole overtime to just get pucks on net," Connor said. "So shot that one and yeah, that one feels pretty good."
Between periods, the Jets cracked jokes, chugged water and snacked on bananas and energy bars.
"You've got to keep it light because it's obviously a very tense situation," captain Blake Wheeler said. "But we've had a good vibe in our room all year so you just try to keep it light and keep everyone loose and keep everyone hydrated - and tell the young guys like Kyle to get going and put an end to this thing."
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 Monday night with a 2-1 victory.
So before the next round, the Jets will get some much-needed rest after playing three straight overtime games - including two on back-to-back nights. The long game Monday had weary players gasping for air when they headed to the bench.
"I give our players credit, they battled hard," Oilers coach Dave Tippett said. "That's not an easy game. We didn't get the result we wanted last night, you come in here and we've got to play a back-to-back. We had a lot of players play very well. It's just disappointing we couldn't get the win."
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.
"It took all pieces of our game," Jets coach Paul Maurice said. "I think the idea going into the series was that the regular season was a tell somehow, and I didn't feel that way. I think (Edmonton) is a very, very good team ... (with) the two best offensive players in the world (in McDavid and Leon Draisaitl). In a bunch of those games, it was very, very close. And much like the series, right? They're all one-goal games. And there was a piece to our game that got better in each one of those."
Maurice called back-to-back games in the postseason "egregious." Asked to describe his emotions, he said: "Well, exhaustion tonight."
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 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 backhand into the top corner.
The Oilers took their first lead 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.
TV cameras caught McDavid shaking his head in frustration on Edmonton's bench.
"I think we're a group that expects more from ourselves. We're a group that we want to push and continue to grow," McDavid said. "And obviously we didn't do that in the playoffs. We're still sour. I don't think anyone's going to deny that."
Wheeler took a shot in the groin late in the third and headed straight to the dressing room bent over in pain. He was back on the ice for overtime. "I've got three beautiful kids, we're not having any more, so what the hell," he said with a laugh. ... Oilers defenseman Darnell Nurse logged 62 minutes, 7 seconds, the third-most in NHL history since statisticians starting tracking playing time. ... It was the Jets' first series win since 2018, when they beat Minnesota in five games and then Nashville in seven before losing to Vegas in the conference finals. ... This was the first postseason series between the teams since 1990, when Edmonton won in seven games in the Smythe Division semifinals.