Anze Kopitar and Kevin Fiala scored for the Kings (25-15-6), who had won three in a row. Jonathan Quick allowed four goals on 27 shots.
"I don't think it was disappointing that we didn't show up tonight and play good enough. I think it was disappointing that we didn't score on our chances," Los Angeles forward Adrian Kempe said. "Power play was good. We didn't get enough at 5-on-5 I guess, and that's a different type of frustration tonight."
Fiala put the Kings ahead 1-0 at 6:32 of the first period, tapping in a backdoor pass from Kempe on a power play.
Tomas Tatar tied it 1-1 at 12:51 with his own power-play goal, scoring from the slot after the rebound of Hughes' shot bounced off Nico Hischier.
Haula gave the Devils a 2-1 lead at 2:37 of the second period when he elected to shoot from the right circle on a 2-on-1.
"I think we could say that we got away with the first a little bit," Haula said. "They put us on our heels, and [Blackwood] was fantastic today. So we came in here 1-1, and then we just figured it out."
Kopitar tied it 2-2 at 6:48 on a power play, but Nikita Okhotiuk responded to put New Jersey back in front 3-2 at 7:40 with a shot from the edge of the left circle that went under the right arm of Quick.
"We'd gone a spell there, we were giving stuff up real quick, and we'd cleaned that up significantly, in my opinion," Kings coach Todd McLellan said. "But 82 games, there's going to be nights when it comes back to haunt you, and tonight was one of them."
Graves made it 4-2 at 10:57 when his bouncing shot from the left point redirected in off Kings defenseman Sean Walker.
"Kind of a freaky goal, a fluky goal, I guess, of mine that finds a way in," Graves said. "It makes a team hard to beat when you're getting scoring from areas you don't usually get it from."
Blackwood kept it a two-goal game when he saved Fiala's penalty shot at 7:19 of the third period.