"We have to find a way to play the whole 60 minutes," Doan said. "We kinda dropped the ball in the beginning of the third period and that's unacceptable."
Ed Jovanovski had a goal and two assists, and Joel Perrault and Daniel Winnik also scored for the Coyotes, who blew a two-goal lead over the first 8:38 of the third period before pulling out their second straight win.
The Coyotes were unable to score during a minute-long two-man advantage. But Vrbata took a pass from Jovanovski near the end of the second Kings' penalty and beat Jason LaBarbera from the right faceoff circle to break a 3-3 tie.
"It was a tight game and we had an opportunity there with the power play 5-on-3," Vrbata said. "It took a little longer than we would have liked to score that goal but I'm just glad we did."
Los Angeles had rallied from a 3-1 deficit entering the third period. Phoenix left wing Daniel Carcillo was whistled for unsportsmanlike conduct as he left the ice for the second intermission and the Kings capitalized 37 seconds into the power play when Brown put a short wrist shot past goalie Ilya Bryzgalov.
Frolov tied the game at 8:38 of the third on a rebound from the low slot following a scramble in front of the net.
"In order to win in these types of game when the stakes get a little bit higher, you have to make sure you're ready to battle, ready to compete, finish checks and pay the price in front of the net," said Kings coach Marc Crawford. "Those are the types of things that win. We got those goals because of those kind of efforts."
Jovanovski gave Phoenix a 1-0 lead on a power-play goal from the high slot at 5:50 of the first period against Los Angeles goalie Dan Cloutier.
"This time of year special teams are going to decide games," Jovanovski said. "L.A. is a little bit passive and it gives us more opportunity to handle the puck."
Ivanans tied the game at 8:30 of the period on a wrist shot from the right faceoff circle.
Perrault put Phoenix back ahead 2-1 at 15:29 when he one-timed a pass from Shane Doan off the bottom of the crossbar from the bottom of the left faceoff circle.
Winnik extended the lead at 6:44 of the second period when he faked Cloutier to the ice with a forehand move, pulled the puck back and bounced a backhand shot off the skate of Kings defenseman Brad Stuart.
"We seem to have a little more structure in the offensive zone right now," said Phoenix coach Wayne Gretzky. "I give our guy credit. They battled."
Cloutier, making his second start since a February 7 recall from the minors, stopped 18 of 21 shots over the first two periods before leaving with what Kings coach Marc Crawford termed "flu-like symptoms" and being replaced with LaBarbera.
"He almost passed out walking out to the rink," Crawford said. "It was tough for Dan. I thought Dan played pretty well."
The win was Gretzky's 99th. ... Doan finished with two assists and has two goals and four assists in his last three games. ... LaBarbera has appeared in 22 of Los Angeles' last 23 games, including twice in relief. ... Ivanans' goal was his first since Dec. 1, against Colorado.