The Kings finish their New York metropolitan area trip with a game Sunday at Madison Square Garden against the Rangers.
"The confidence was there after winning on the island," Scrivens said. "It's obviously important to stop every shot."
Scrivens came up with 12 saves in the first period when he was tested by the Devils.
"We probably deserved to have one or two in the first period," Devils coach Pete DeBoer said. "We just didn't take advantage in the first. We're not a pretty group offensively. We have to score some ugly goals. We all feel for (goalie Cory Schneider). He can't do more than what he's doing. It's frustrating for all of us."
King's sixth goal of the season came at 13:08. Defenseman Jake Muzzin's drive from the left point was redirected by King, standing in front of Schneider.
"It came off a line change," King said. "They were battling on the wall and it got to the point, I was wide open at the net and he slid one on the ice and I got a stick on it. We came back last night and tonight. We had to find a way to win, and that's what good teams do."
Kopitar scored an empty-net goal with 2.9 seconds left. Schneider made 19 saves.
"He's a solid goaltender," Kopitar said of Scrivens. "We got off to a little bit of a slow start and we kept building up our game, making plays. Eventually in the third, we got one."
Friday's game was the Kings' first visit to the Prudential Center since playing the Devils in the 2012 Stanley Cup finals.
The Kings nearly scored 7:33 into the third period. Muzzin centered a puck from the left side of the blue line. New Jersey defenseman Andy Greene put out his stick and deflected it on goal, where Schneider alertly made the save.
In the second period, defenseman Peter Harrold was whistled for a four-minute penalty when he was called for high sticking Tyler Toffoli of the Kings.
But King was penalized for hooking 50 seconds into the power play and sat for two minutes.
Harrold was the recipient of a hit to the head by Jordan Nolan with 1:31 left in the second.
The center put his shoulder down and leveled Harrold with a shot to the side of his head. Harrold was face-down on the ice, but, after play was stopped, he managed to skate off on his own. Harrold returned to regular shifts in the third period.
The Devils were the aggressors in the scoreless first period but couldn't solve Scrivens.
"(Schneider) has played unbelievable for us so far this year, and we haven't given him the goal support," Devils winger Stephen Gionta said. "I thought we played a pretty good controlled game in their end, but we could have gotten to the net a little more."
The power-play goal by Kopitar in the closing seconds broke a string of 12 straight kills over three games by the Devils. ... Jaromir Jagr has 120 career game-winning goals, just one behind the NHL record held by Gordie Howe. ... Patrik Elias returned after a six-game absence for the Devils, who also got back Gionta.
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NEWARK, NJ - NOVEMBER 15: Mark Fayne #7 of the New Jersey Devils sends Dustin Brown #23 of the Los Angeles Kings...