Blake Wheeler, Dustin Byfuglien and Patrik Laine scored for the Jets (35-16-9, 79 points), who had their three-game winning streak ended. They are two points behind the Nashville Predators for first place in the Central Division.
"They picked up their speed a little bit, some untimely penalties. The penalty kill is kind of leaking oil right now," Wheeler said. "Just kind of wrong penalties at the wrong time. They capitalized, stole some momentum. Still 2-2 going into the third at home, I don't think we hate that spot. Just weren't able to get one early enough to go in the third."
Wheeler made it 1-0 at 5:46 of the first period with a wrist shot from the right circle on a 5-on-3.
Martinez scored on the power play at 1:49 of the second period to tie it 1-1, beating a screened Hellebuyck with a shot from the point.
"They had some really good screeners in front of me," Hellebuyck said. "I found myself up high a lot. Give them credit, they're a good team. They've won a couple of Stanley Cups for that reason, they know how to screen a goaltender. It makes a world of a difference."
Phaneuf gave the Kings a 2-1 lead with a goal on the power play at 17:05. He has three goals in four games since being traded to the Kings from the Ottawa Senators on Feb. 13.
"Dion's been a good fit there," Kings coach John Stevens said. "He wants to shoot the puck all the time. He's always looking at the net. I think he's got people going there because they know the puck's going to go there."
Byfuglien tied the game 2-2 on a one-timer from the point that deflected off the stick of Kopitar at 18:55.
Laine cut the lead to 4-3 with 48.5 seconds remaining in the third with his NHL-leading 16th power-play goal.