The Coyotes (22-25-6) lost their 11th in 14 games (3-10-1) and fell to five points behind the St. Louis Blues for fourth place in the Honda West Division. The Blues won 3-1 against the Anaheim Ducks on Monday. The top four teams make the Stanley Cup Playoffs.
The Blues need two points in their final six games or for the Coyotes to lose one of their three remaining games to clinch a playoff berth.
"Anything can happen," Coyotes forward Lawson Crouse said. "We have to go right to the end. … That's all we can really ask, get as many points as you can, because you never really know until the last regular-season game ends."
Christian Dvorak and Jakob Chychrun scored, and Darcy Kuemper made 23 saves for Arizona.
Jonathan Quick made 17 saves for the Kings (20-24-6) before leaving with an upper-body injury after the second period. Cal Petersen played the final period and made 15 saves. Trevor Moore scored.
Kings coach Todd McLellan said he liked how his players responded to a 6-2 loss to the Ducks on Saturday.
"I thought we were aggressive, we tried to take the game to them rather than receiving it," McLellan said. "We were able to stay ahead of them with line changes, so we were the fresh five rather than the tired five, which makes a big difference for our team. And we were just aggressive."
The teams play here again Wednesday.
Iafallo gave the Kings a 3-2 lead on a power-play goal at 13:40 of the second, scoring off a rebound of Drew Doughty's slap shot from the right point that Kuemper couldn't cover.
Kopitar had tied it 2-2 at 7:40 on a rush with Adrian Kempe.
Iafallo and Kempe switched lines, with Kempe moving up to Kopitar's line, and McLellan liked how both played with their new linemates.
"They flipped positions and I thought they both played really well," McLellan said. `Al' has been snakebit a little bit, he hasn't been getting on the scoresheet, so to get the winner on the power play is a nice sign for him."
Chychrun's 17th goal, the most among NHL defensemen, gave Arizona a 2-1 lead on a power play 53 seconds into the second period. Conor Garland, who missed the previous six games with a lower-body injury, had the primary assist.