Jarvis put Carolina up 1-0 at 3:00 of the first period, scoring off a pass from Aho on a 2-on-1.
Lizotte tied it 1-1 at 4:38 with a wrist shot through traffic from the left face-off circle.
The Hurricanes retook the lead 10 seconds later when Stepan had the second tip of Brady Skjei's shot from the blue line, making it 2-1 at 4:48.
Kempe tied it 2-2 at 12:39, redirecting Alexander Edler's shot from the left point off a face-off win by Anze Kopitar.
Olli Maatta's goal for Los Angeles at 19:40 was overturned following a challenge by Brind'Amour for goaltender interference. It was determined Kings center Phillip Danault made contact with Andersen in the crease prior to Maatta's shot into an open net.
"I'm happy that we had the offense that we had tonight, and there could have been more," Los Angeles coach Todd McLellan said. "Again, with the 2-on-1s and not even getting a shot on goal, goal called off. Could we avoid the goaltender? Maybe he makes the save then. But there could have been more, so that's the positive of the night is that the offense was there."
NOTES: The five go-ahead goals tied the Hurricanes/Hartford Whalers record. Hartford did it in in a 6-5 win against the New York Rangers on Feb. 22, 1981, and in a 5-5 tie against the Buffalo Sabres on Feb. 24, 1991. … Necas has scored five points (two goals, three assists) during a three-game point streak. … Andersen had the secondary assist on Aho's goal. It was the goalie's second assist of the season and 11th of his NHL career. … Edler had two assists for his first multipoint game with the Kings. The defenseman signed with Los Angeles in the offseason after playing his first 15 NHL seasons with the Vancouver Canucks.