"We're showing a lot more fight and a lot more resilience right now so it should go a long way for the team," said Nugent-Hopkins, who scored his ninth goal of the season.
It was a seesaw game, a trend that continued in overtime. The Coyotes dinged two posts and the Oilers got chances from odd-man rushes but it was Nugent-Hopkins in alone that ended the match.
"I had a lot of time to think about it but I didn't want to over-complicate it," the forward said. "I just tried to get my best angle to put that low blocker there."
Coming into Tuesday's match, the Oilers were 1-10-0 when trailing after 40 minutes. The club trailed 2-1 heading into the third period, improving the stat to 2-10-0 with Matt Benning's game-tying goal at 14:25 of the third period and Nugent-Hopkins' overtime-winner.
Zack Kassian rounded out the scoring with his first of the season in the opening period.
Oilers keeper Cam Talbot made 29 saves, finishing the night with a .935 save percentage.
"He made some dangerous scoring chance-type saves early in the game," said Oilers Head Coach Todd McLellan. "The work that he did get was dangerous, especially in overtime."
Edmonton threw 27 shots on goal, won 48 percent of their faceoffs and finished the night 0-for-3 on the power play.
The Oilers had an opportune chance to open the scoring in the first period - on a crisp passing play by Leon Draisaitl, Drake Caggiula and Ryan Strome - but Christian Fischer did so instead.
The Coyotes forward planted himself in front of the Oilers net and whacked at a loose puck that Talbot couldn't snare, scoring at 6:22 of the first period to give the 'Yotes a 1-0 lead.
The goal marked the 17th time the Oilers had allowed the first goal against in a game this season but the club did even it up.
After a Clayton Keller hooking penalty, Kassian made good on a breakaway.
Mark Letestu head-manned the puck for the winger, sending him in all alone on Scott Wedgewood. Kassian went blocker side for his first of the season and his sixth point at 16:30 of the opening frame. The goal came on Edmonton's fourth shot of the game.
The two clubs swapped opportunities in the second period.
Wedgewood first made a clutch catch on a doorstep chance by Kassian.
At the other end of the ice, Talbot stopped Oliver Ekman-Larsson on three consecutive goalmouth shots to shut the door.
But the defenceman's fourth crack at the net gave the Coyotes a 2-1 lead.
Oilers forward Strome was called for slashing in the offensive zone with less than two minutes to play in the middle frame. Ekman-Larsson scored on the ensuing power play by releasing a one-timer top right to give Arizona the lead with 48 seconds left on the clock in the period.
The Oilers played desperate in the final period and eventually tied the game up with a Benning whistler from the point at 14:25. The goal was Benning's third of the season. Milan Lucic and Kris Russell got the assists.
"If you see the way that we played in the third period, it's just frustrating we can't do that all the time," said Strome.
Edmonton has now won three of their last four games. The club will host the Toronto Maple Leafs Thursday at Rogers Place. Puck drop is 7:08 p.m. MST.
"We'll look at the game and we'll be critical with our team in certain areas and we'll be happy in another," said McLellan. "At the end of the day, it's a win. It gives us a chance to come out and play Thursday to try and extend a winning streak."