The Rangers were hoping to build on their 3-2 win at the Buffalo Sabres on Wednesday. They loved their start in that game, but did not like the way they played in the third period.
That carried into the first period Saturday, with the Rangers lamenting their effort and execution.
"It was a horrendous first period," coach Peter Laviolette said.
Turcotte gave the Kings a 1-0 lead at 7:05 of the first period, scoring on a 2-on-1 with Kempe.
Turcotte moved up to play on the top line with Kempe and Kopitar because Trevor Moore was out with an upper-body injury.
"I thought he had a really good game," Kings coach Jim Hiller said. "What a great finish. Just a nice goal all three coming up the ice. I thought he was real good. I thought he was one of the stars of the game for us."
The Kings second line of Byfield, Foegele and Tanner Jeannot, combined for two goals, three assists and nine shots on goal.
"We needed that," Hiller said. "I thought their line was flat in Jersey. They didn't get anything done. Against a good team you can't have one line flat. They came out and they were flying. There's no question they set the tone for us as a line."
Foegele gave Los Angeles a 2-0 lead at 15:06, scoring on his own rebound from the slot after getting the puck from Byfield.
The Kings then scored three goals in the first 5:04 of the second period to take a 5-0 lead.
"To start a game like that in our building after playing some of the games like we have in our building, it's bad," Laviolette said. "You know what I mean, it was a bad start. Right from the very beginning, the puck movement, the speed in which we were playing, the strides, completely different from where we were a game ago. We can't just play one game like that; we've got to string together 10 games like that. So consistency in what we're doing is not good. It's frustrating and disappointing to start the game like that."
Byfield's one-timer from above the right hash marks off a pass from Foegele gave Los Angeles a 3-0 lead at 2:46. It was his first goal in nine games.
Kempe finished off a pretty passing sequence between Turcotte, himself and Kopitar to make it 4-0 at 4:40.
Phillip Danault scored off a rebound of Brandt Clarke's shot 24 seconds later, extending the lead to 5-0 at 5:04, giving the Kings three goals in a 2:18 span.
"We talked about let's have a good push in that first five minutes of the second," Foegele said. "We certainly did. We kind of just ended the game there."