Petr Mrazek made 22 saves for the Hurricanes (34-23-6), who are tied in points with the Pittsburgh Penguins for third place in the Metropolitan Division.
Dougie Hamilton had two goals and an assist, and Jordan Staal had three assists for the Hurricanes, who have won three in a row and are 12-3-1 in the past 16 games.
"When we're getting pucks in and forechecking and our forwards just buzz, it's really hard to play against," Hamilton said. "It's a lot of fun for us."
WATCH: [All Kings vs. Hurricanes highlights]
The Kings (23-33-7) are 0-6-3 in their past nine games, their longest losing streak since going 0-10-0 from Feb. 22-March 9, 1984. Jonathan Quick allowed six goals on 20 shots in two periods and was pulled from his second consecutive start. Jack Campbell made 14 saves in relief.
"We've got to be better in front of [Quick]. That's all there is to it," Kings coach Willie Desjardins said. "It's not fair to him."
Hamilton's 11th goal of the season gave the Hurricanes a 1-0 lead at 5:56 of the first period. Quick was caught behind the net after a collision with Saku Maenalanen, and Hamilton shot into an open net.
Teravainen forced a turnover in Carolina's defensive zone that sent Sebastian Aho on a 2-on-1 for his 25th goal and a 2-0 lead at 11:15.
"We just worked pretty hard," Teravainen said. "We got a lot of loose pucks and turned the puck over from them. I think that's how we got all our chances."