Anze Kopitar scored into an empty net to make it 4-2 with 1.7 seconds remaining. It was his 35th goal, setting a new NHL career high after he had 34 in 2009-10.
Jack Campbell made 20 saves for his second NHL win, and Tyler Toffoli and Drew Doughty each had two assists for Los Angeles, which is 4-1-1 in its past six and has won consecutive games for the first time since winning three in a row Feb. 17-20.
Defenseman Kevin Connauton scored for the second straight game, and Max Domi had a goal and an assist for the Coyotes (27-40-11), who lost for the first time in three games. Darcy Kuemper made 31 saves.
Carter, who has scored in three straight games, has five goals and two assists during a four-game point streak. He has 13 goals in 17 games since returning from surgery to repair a torn tendon in his ankle.
Carter tied the game 2-2 with a power-play goal at 11:49 of the second period. Dion Phaneuf shot from the blue line after keeping the puck in the Coyotes zone, and Carter was in the slot to redirect it for his 59th multigoal game in the NHL.
"It's just his presence in a lot of areas checks a lot of boxes, but he's a production guy," Stevens said. "He ends up in the scoring areas, he goes to the tough areas. He scores goals that other guys can't."
Domi put the Coyotes ahead 2-1 at 5:14 of the second when he scored on a backhand following Christian Dvorak's wraparound shot. Trevor Murphy got his first NHL assist and second point in his fourth game in the League.
After Connauton gave the Coyotes a 1-0 lead at 12:26 of the first period, Carter tied it 1-1 with 28 seconds left in the period, tipping Derek Forbort's shot past Kuemper for his 350th NHL goal.
"That's a team fighting for a playoff spot, a lot of experience," Domi said. "I think that can go in the memory bank and find ways to win that next year. It's a good test for us, but a really good learning experience too."
