Conor Garland had a goal and an assist, and Christian Dvorak and Nick Schmaltz each had two assists for Arizona (13-7-2), which has won four of its past five games.
The shutout was the Coyotes' second straight; Darcy Kuemper made 37 saves in a 3-0 win against the Calgary Flames on Saturday. It's the first time Arizona has had consecutive shutouts since a three-game streak from March 29-April 3, 2012.
"We've got a 1-2 punch here that's pretty special," Coyotes coach Rick Tocchet said.
WATCH: [All Kings vs. Coyotes highlights]
Jack Campbell made 24 saves for Los Angeles (8-12-2), which went 0-for-4 on the power play.
"We were just too slow, our feet weren't moving, and our mind wasn't as sharp as it needed to be," Kings captain Anze Kopitar said. "It seems like we were a half step too slow, a couple of feet off, which in the big picture is obviously big and was the difference."
Garland scored his Coyotes-leading 10th goal at 3:12 of the first. Dvorak took the puck from Kurtis MacDermid in the slot and swept it to Garland for a tap-in to give Arizona a 1-0 lead.
"We got off to a great start, and I think we played pretty smart the whole way through," Raanta said. "Our [penalty kill] was really good, and obviously the power play got a couple of goals, and that's nice because that always gives you confidence. … They had a three-game winning streak, and you know it's not going to be an easy game."