Jonny Brodzinski, also a former King (2017-19), scored his first goal of the season and had an assist, and Vincent Trocheck had three assists for the Rangers (19-6-1), who ended a two-game losing streak.
The Rangers lost 4-0 to the Washington Capitals on Saturday and 6-2 to the Ottawa Senators on Tuesday.
"There were some negative things creeping into our game," Trocheck said. "We all knew it and we recognized it, and I think that the biggest thing is just making sure you can spot it whenever it's coming and get to it quickly. I thought we had a really good bounce back game tonight against a really good hockey team."
Phillip Danault scored, and Pheonix Copley made 23 saves for the Kings (16-5-4), who lost a road game in regulation for the first time this season. Their NHL-record 11-game road winning streak to begin the season ended Saturday in a 3-2 overtime loss at the New York Islanders.
The Kings finished their four-game road trip 2-1-1. They play at home against the Winnipeg Jets on Wednesday.
"A lot of things have been going our way, so it's nice to have a little adversity," Los Angeles defenseman Mikey Anderson said. "We've got faith in our leaders, the guys that have been here a long, long time. They right the ship. I don't think there is going to be any sense of panic or anything in the group. We trust what we have here. We trust what we're doing. Get back in L.A. and get back to working, figure some things out."
Mika Zibanejad gave New York a 1-0 lead with a power-play goal at 8:27 of the second period when Artemi Panarin moved the puck to Trocheck in the right circle, who passed across to Zibanejad in the left circle for a one-timer.
Jimmy Vesey made it 2-0 at 17:27. Nick Bonino leaped to hold the puck in at the blue line and passed down low to Vesey, who deked to his backhand and put the puck through Copley’s five-hole.
"There was not a lot of room the first period to do anything," Laviolette said. "I think we just stuck with it and eventually generated some good chances in the second period and continued to push in the third. For me, just a really good start to finish game."