Antti Raanta made 40 saves for his first win since Feb. 4 for the Coyotes (10-9-3), who won their fourth straight road game.
"On the road, especially when there's fans, you try to simplify it a little bit and get it in behind them a little more," Schmaltz said. "We always play hard on the road. I don't know what it is. We've got to try to bring it back home and make Arizona a tough barn to play in."
Drew Doughty and Gabriel Vilardi scored, and Jonathan Quick made 20 saves for the Kings (9-8-4), who have lost three straight following a six-game winning streak.
"Obviously our penalty kill let us down tonight," Los Angeles coach Todd McLellan said. "We made two critical mistakes, and they capitalized on the mistakes that we saw last year in our penalty kill. We think we've corrected them and they're creeping back in, so we've got work to do there. Our inability to get clears was something that I'm really disappointed in. We couldn't get fresh bodies out because we couldn't get the puck all the way down."
Arizona was 2-for-3 on the power play; Los Angeles was 1-for-4.
The Kings have been much improved on the penalty kill this season, coming in with 11 straight kills in the past four games to rank fifth in the NHL at 85.9 percent (55-for-64), but the Coyotes have been one of the few teams able to take advantage.
Arizona is 4-for-10 on the power play in three games against Los Angeles this season.