The Coyotes, who have resided at or near the bottom of the NHL for most of the season, posted their fifth win in seven games and 11th in the past 16. The Kings absorbed only their third loss in the past eight games.
Arizona led 3-0 midway through the second period before Los Angeles rallied to force overtime.
Rookie Arizona goaltender Adin Hill stopped 34 of 37 shots for his first career NHL win. Hill, a 21-year-old Comox, British Columbia native, made only his third NHL appearance as Darcy Kuemper was rested after four straight starts.
Kings goaltender Jack Campbell recorded 26 saves on 29 shots. Campbell, a 26-year-old Port Huron, Mich., native, made only his second start of the season as Jonathan Quick received a night off after the Kings shut out Vancouver on Monday.
Tuesday's contest was only the fifth all-time NHL appearance for Campbell, who was selected by Dallas in the first round (11th overall) of the 2010 draft but has toiled mostly in the minors.
Keller opened the scoring 5:08 into the game, beating Campbell with a shot through the legs. Cousins doubled Arizona's lead at 15:43 of the opening stanza as he spun around and put a shot in off Doughty's skate.
Dvorak gave the Coyotes a 3-0 lead at 10:13 of the second period, sending a high shot over Campbell after the Kings turned over the puck in their zone. However, Pearson reduced Los Angeles' deficit only 27 seconds later as he culminated a Kings rush by putting home a high shot from the slot.
The goal was Pearson's second in two nights and gave him points in five of the past six games.
Carter's first goal of the game brought the Kings within one during a power play at 12:03 of the third period. He deflected in Doughty's shot. The Kings got the power play after the Coyotes had too many players on the ice.
Carter's second tally, with 2:18 left in the third period, forced overtime. The Kings received a power play 23 seconds into the extra session, when Richard Panik was penalized for tripping Carter, but they could not score.
Arizona's Keller and Los Angeles' Adrian Kempe traded shootout goals before Goligoski decided the outcome.
--Field Level Media