Nurse picked up the puck in the neutral zone before working his way twoard the Jets zone before sidestepping a check and beating Jets goaltender Connor Hellebuyck short side with a wrister.
"I was trying to make a read and you know just have confidence to try and make a play," said Nurse of his overtime tally. "At the same time the guys helped me out. They allowed me to skate. It was a lot of fun."
"It was a huge team win tonight. The guys set the tone early in the third and got us back in this game and it feels good to be able to contribute at the end," he added.
The game winner capped a four-goal comeback for the Oilers, who seemed resigned to a road loss on their final game of a four game road trip before storming back.
Connor McDavid drew in all four goals in regulation, with two goals and two assists while setting an NHL record in the process.
The Edmonton star has been in on the first nine goals of his club's season.
But he isn't buying into the hype.
The previous record was 7, set by Adam Oates in 1987.
"You know what it's a record," said McDavid. "I'm not really proud of it. I don't think it's a stat you should be proud of either. It is what it is. We found a way to get a goal at the end."
Jets captain Blake Wheeler said the Jets should have locked the game down.
"Yeah, 4-1 should be game over. Our line went out, gave up one early on and gave them momentum. You’re fighting an uphill battle from there," said Wheeler. "They just got that first one real quick [and] all of the sudden there is life on their bench, we’re on our heels a little bit, momentum was all on their side, pop a power-play goal so then we’re reeling. We just let the momentum get away from us, just couldn’t turn it around.”
Ty Rattie and Jesse Puljujarvi had the other Oiler goals.
Leon Draisaitl and Ryan Nugent-Hopkins each had two assists.
Ben Chiarot and Mark Scheifele also scored for Winnipeg.
Connor Hellebuyck made 28 saves for the Jets, who continue their six-game homestand on Thursday against Vancouver.
Cam Talbot turned aside 29 shots for Edmonton, who return home to begin a four-game homestand against Boston.
Things looked good for Winnipeg early on as Adam Lowry staked them to a 2-0 lead before the game was eight minutes old.
Lowry, the Jets third line centre got Winnipeg on the board just under the five minute mark when he took control of a puck along the end boards, walked out in front of the net and tucked the disc just under Edmonton goaltender Cam Talbot's pad.
Lowry scored again just under three minutes later when he followed up on his own rebound, depositing a puck past Talbot to put the Jets up 2-0 at 7:47.
McDavid pulled the Oilers to within a goal at 12:49 on the power play.
McDavid took a feed from Leon Draisatl along the left side boards by the Jets blue line before breaking in and depositing a backhand shot past Connor Hellebuyck.
The goal was his third of the season.
Ben Chiarot restored Winnipeg's two-goal cushion just 22 seconds later when he took a drop pass from Nikolaj Ehlers, who was crossing the zone at the top of the faceoff circle before blasting a slapshot from the point just inside the left goalpost.
With the Oilers serving a bench minor for too-many-men, Mark Scheifele pounced on a rebound off of a Patrick Laine shot before snapping the puck past Talbot.
The goal was his second of the season.
Ty Rattie pulled Edmonoton to within a pair just eighteen seconds into the third after Connor McDavid broke in and left a drop pass for him which he buried just under the cross bar to make it 4-2.
The goal was his first of the season.
Connor McDavid fired a puck past Hellebuyck on the power play to pull the Oilers within a goal at 2:28 of the third.
With Andrew Copp off for holding, Ryan Nugent-Hopkins got a shot on goal and Hellebuyck kicked the puck right onto the waiting stick of McDavid, who was about fifteen feet out on the right side. The Oilers captain made no mistake, firing the disc past the Jet goaltender to make it 4-3.
Jesse Puljujarvi tied the contest at 13:39 of the third when he put his stick down while driving the net.
Ryan Nugent-Hopkins hit the blade Puljujarvi had his first goal of the season.
SHOTS-EDMONTON 35 WINNIPEG 33