Nugent-Hopkins scored late in the third period to lead the Oilers to a 3-2 win against the Tampa Bay Lightning at Rexall Place.
The Oilers center snapped a shot past Lightning goaltender Ben Bishop with 3:25 left in regulation following a turnover in the Tampa Bay zone.
"I thought we really battled hard," Nugent-Hopkins said. "They tied it late and we had a really good pushback, so it was really good to see.
"Our line [Taylor Hall and Jordan Eberle] just got back together and we wanted to establish ourselves early in the game and we want to be the driving force for the team out there. We take that pressure on ourselves every night, especially when we're together. I thought we did a good job of handling that [Monday]."
Shortly after the Lightning tied the game in the third period, left wing Ondrej Palat had his clearing pass intercepted by Eberle inside the blue line. Eberle found Nugent-Hopkins in the slot, where he fired a wrist shot past Bishop.
"[Nugent-Hopkins] was really skating well and Eberle was making plays and it's fun to play with those guys when we're working as a unit like that," Hall said. "Not only our line, but it seemed like every line was getting good chances. It's good to keep the momentum going like that."
Oilers goaltender Ben Scrivens made 22 saves, helping snap a five-game winless streak to start the season (0-4-1). Bishop made 20 saves for the Lightning.
"We have to be better," Bishop said. "We can't come out and play like this on the road and expect to win. We had too many breakdowns all over the ice. We showed some fight in the third, but it still wasn't even close enough to win in this League. We just weren't making any plays. Any time we had the puck we turned it back over. We gave up more odd-man rushes [Monday] than we have had all season. We have to be better."
Boyle opened the scoring at 1:21 of the second period, banking a shot in off Schultz's skate past Scrivens.
Schultz was able to get the goal back at 4:35, lifting a backhand over the shoulder of Bishop. The goal was Schultz's first of the season.
"It was nice, you never want to have a goal scored on you that goes in off you," Schultz said. "It was nice to go down there and score. I got a lucky bounce off his knob there. It worked out and it was nice to get the win."
The Oilers went ahead at 14:57 of the period with Hall's penalty shot. Hall had been sent in on a breakaway on a long pass out of the zone from defenseman Mark Fayne. Hall was unable to get a clean shot on net, hooked from behind by Matt Carle.
Hall went in and slipped the puck between the pads of Bishop to score the go-ahead goal. It was Hall's fourth goal of the season. He also had an assist.
By converting on the attempt, Hall became the fifth Oilers player to score on a penalty shot at Rexall Place, joining Wayne Gretzky, Craig MacTavish, Doug Weight and Ryan Smyth.
Prior to going in on his attempt, Hall lifted his arms in the air in an effort to fire up the crowd.
"I just wanted to do something to take my mind off the shot and let me relax a little bit," Hall said. "It seemed like the fans liked it. I'm glad I was able to score."
In the third period, Connolly tied the game at 13:55, taking a pass from Tyler Johnson in the slot and firing a shot past Scrivens. Prior to the goal, Bishop made a pad save on Leon Draisaitl from close range to keep the Lightning within one.
"In the third, I thought we played desperate," Lightning coach Jon Cooper said. "If we had played that way in the first two periods, who knows how the game turns out. In the end, we were playing a desperate team. They have had some breaks go against them this year and [Monday] they all went for them.
"They got some breaks, but they earned them. I'm not sure for a couple of periods that we earned ours. Our desperation level is just not there."
Nugent-Hopkins restored the lead with his first goal of the season.
Charged with going head-to-head against Stamkos, Nugent-Hopkins helped to keep the Lightning star off the score sheet.
"He's a guy who can take advantage, if you give him an inch, he can put the puck in your net," Nugent-Hopkins said. "I thought we did a really good job, not just our line, but every line that was out there against him.
"It's good to go up against guys like that, they definitely push you to play better. Playing against him, we have (Alex) Ovechkin coming up here and (Sidney) Crosby a little bit later. Those kinds of guys, they really make you play your best. I thought we did a really good job of handling him [Monday]. Obviously he's a great player, he still had some chances, but we did a good job of limiting his chances."
Left wing Jonathan Drouin, the third player selected at the 2013 NHL Draft, made his debut for Tampa Bay and had one shot on goal in 16:10. Drouin was inserted into the lineup after Alex Killorn sustained an injury during the morning skate.
Lightning right wing Ryan Callahan did not play in the third period because of a lower-body injury.
The Lightning will play the third of their five-game road trip Tuesday at the Calgary Flames; the Oilers continue their seven-game homestand Wednesday against the Washington Capitals.