Rob Klinkhammer and Mikkel Boedker scored 63 seconds apart in the first period for the Coyotes, who handed the Kings their third consecutive loss and took over sole possession of eighth place in the Western Conference. Mike Smith made 36 saves.
"Smith was a really strong player for us tonight. It's a good thing he showed up to play. He had one heck of a game," coach Dave Tippett said. "When you need things done to win a game, guys like [Antoine] Vermette, [Lauri] Korpikoski, and [Zbynek] Michalek are the people to get it done for you. Some people competed very hard for us and we were able to pull out a win."
Marian Gaborik, defenseman Alec Martinez and rookie Tanner Pearson scored for the Kings, who were without captain Dustin Brown for a second successive game because of a lower-body injury. Jonathan Quick stopped 23 shots for Los Angeles, which fell to 21-1 when leading after two periods.
"I thought they were desperate the whole game, like the way they are in the playoffs. That's the time of year it is. Everybody is playing desperate," said Quick, who was 6-1 with a 1.28 goals-against average in his previous seven games. "I thought we played well enough. I don't think I played well enough. When you give up four goals, you're going to lose the game. I've got to be better."
Yandle tied it with a slap shot from just inside the blue line after he intercepted defenseman Matt Greene's attempted clearing pass from behind the net. Greene was a healthy scratch in the previous eight games.
"It comes down to having to play a full 60 minutes. We didn't do that," Martinez said. "We had a few breakdowns defensively and we can't have that in the third period, especially against a good team. It's a battle in the West. We have to sharpen up."
Halpern put Phoenix ahead 4-3 with a shot from the left circle that appeared to carom off Quick's glove and then the post before it bounced to Coyotes captain Shane Doan for another point blank shot that Quick stopped with a sprawling save.
But an overhead replay showed that Halpern's shot crossed the goal line before it hit Quick's stick.
"We have the headset on the bench, so we got a call from our video guy saying the puck was in. So we were just hoping for the right call," Tippett said.
Quick missed a chance to tie Rogie Vachon's franchise record of 171 victories. Darryl Sutter will also have to wait for his 500th regular-season victory as an NHL coach.
"I think we could have been a little bit more desperate on the two goals they scored, in terms of making plays in our own zone," Sutter said. "That is back-to-back games where we have made basic checking mistakes in our own zone. We need some more out of our top guys."
The Kings outshot Phoenix 15-2 in the second period, turning a 2-1 deficit into a 3-2 lead. Gaborik got the puck in the low slot from Anze Kopitar and took a shot that glanced off defenseman Derek Morris' stick and over Smith's glove. It was his eighth goal this season and second in six games since he was acquired from Columbus on Feb. 5.
"Quite honestly, the score should have been quite higher both ways if you look at mistakes that were made and the big saves the goalies had to make," Sutter said.
Smith, who leads in games played, starts, saves and shots faced, withstood an early barrage from the Kings before the Coyotes took a 2-0 lead. Klinkhammer scored his 11th goal on a rebound at 6:33, and Boedker added his 17th during a power play.
"I know how good they are here. They have such a great blue line, and so many good forwards. So it was big for us to find two points in regulation," Doan said.
The Kings got to 2-1 when Pearson, in his third stint with the club this season, scored his second goal in 14 NHL games at 17:02 of the first. Los Angeles tied it at 6:50 of the second with Martinez's eighth goal.
Phoenix's Martin Hanzal, who returned after missing seven games with a lower-body injury, got an assist on Klinkhammer's goal.
The Kings are 126-2-11 in their past 139 regular-season games when leading after two periods. The only other regulation loss was on Jan. 22, 2013 at Colorado. ... Kings F Justin Williams is expected to play in his 200th consecutive game on Thursday. He would become the 13th different player in franchise history to reach the figure, including Kopitar, who holds the club record with 330. ... Gaborik has 21 goals in 30 career games against Phoenix. ... Pearson's first goal came in his regular-season debut on Nov. 14 against the New York Islanders. ... Yandle leads Phoenix with 49 points, including an assist on Boedker's goal.