Darcy Kuemper made 34 saves, including 17 in the third period when the Kings, who trailed 2-1 after two periods, made a strong push to take control of the game. Rookie Carl Grundstrom notched his first NHL goal at 3:44 of the third period to tie the score 2-2.
But the Coyotes responded as Dvorak and Grabner each tallied their second goals of the game 5:06 apart. Dvorak scored his from the top of the crease, and Grabner beat Kings goalie Jack Campbell on a breakaway.
"Once they tied it up we started to push a little more, take over the game, play our game," Grabner said. "I think we let them hang around, played a little tentative at times. A team like that, that has experience like that, will make you pay eventually, and they did. I think we played a lot better once they tied it up."