Nugent-Hopkins wasn't pleased about the Kings' rally, but the Oilers earned their first win after regulation after starting 0-7.
"We can still do a much better job pushing back when a team comes at us hard like that, but at the same time, it was a big game for our morale," he said. "It was great to finally go to a game that goes to extra time this season and come away with the two points."
The Oilers (8-22-7) won for just the second time in 22 games. It was also just the second win of the season for the Oilers against a Western Conference opponent (2-18-6).
Newcomer Derek Roy, acquired in a trade with Nashville on Monday, said he could tell the Oilers were a team in desperate need of a positive result.
"Getting a win is the main thing right now," he said. "We just need to build on it. This should give us some confidence to make plays late in games. We can't allow ourselves to be under siege like we were in the third period.
"The more experience that we get knowing how to win, the better we are going to get."
This marked the first NHL win for Oilers interim head coach Todd Nelson.
"It does feel really good. I'm not sure it has sunk in yet," Nelson said. "It is more or less a relief. It's a relief for everyone to get this win under our belts, and now we can build the result."
Drew Doughty and Jake Muzzin had goals for the Kings (18-12-8), who lost for the second time in two nights and dropped their fifth straight on the road.
"This one is disappointing, just like the last one (a 2-1 loss in Calgary)," Muzzin said. "We have to come out hungrier, more desperate, harder. I don't think we're coming out with the right attitude that we need to win hockey games right now.
"We shouldn't be in that situation where we need goals late. We have to get our goals early."
Edmonton took a 1-0 lead 4:37 into the game as Roy made an impact in his first game with the Oilers.
Roy made a heads-up feed to Hendricks, who fired a shot from the slot past goalie Jonathan Quick. Roy left the game soon afterward when his ankle was cut by a skate. He missed the remainder of the first period but returned for the start of the second.
Edmonton made it 2-0 at 9:32 of the second. Nugent-Hopkins made a kick pass to Taylor Hall and then got the puck back and scored his 11th goal.
The Kings outshot the Oilers 22-16 through 40 minutes.
Los Angeles broke Scrivens' shutout bid midway through the third. Doughty's shot from the point was originally thought to have hit the crossbar, and the game continued for another 34 seconds before a stoppage allowed for a video review.
It was then determined that the puck had struck the camera inside the net.
Kings coach Darryl Sutter said he had a feeling that it would end up being a goal.
"Drew said it was," he said. "(Jeff) Carter said something about the sound of it. He said it didn't sound right. We knew they were going to review it, and at the first whistle we knew the league was going to call back."
The Kings tied it with a power-play goal as Marian Gaborik swung behind the net during a scramble and fed the puck in front to Muzzin, who scored with 2:25 remaining in the regulation.
Los Angeles outshot Edmonton 15-1 in the third period.
Scrivens made 39 saves in the victory. Quick stopped 21 shots.
NOTES: It was the second of five meetings this season between the teams. The Kings beat the Oilers 6-1 on Oct. 14 at Staples Center. The Kings entered the game with seven consecutive wins over Edmonton. ... Matt Fraser also made his Oilers debut after being picked up on waivers from the Boston Bruins. ... It was the first game that Nelson had the bench to himself, as general manager Craig MacTavish returned to the press box.