Martin Frk had a power-play goal in his season debut, Dustin Brown scored in his return, and Jonathan Quick made 16 saves for the Kings (16-13-5).
"If you look at our 5-on-5 play, I think we outplayed them the whole night from start to finish," Brown said. "Give up two power-play goals and [an] empty-net [goal], it's one of those games where 5-on-5, I think we were the better team, but it's not always the way it goes."
Matt Luff, who played his first three NHL seasons with the Kings, scored his first goal for the Predators at 2:49 of the second period for a 3-0 lead. Luff signed a one-year contract July 28.
"Had a tough couple years there, and to get one [point] there is huge," said Luff, who scored 17 points (10 goals, seven assists) in 64 games with Los Angeles.
Saros saved Adrian Kempe's penalty shot at 5:06 after the Kings forward had been held by Predators defenseman Alexandre Carrier.
"I like when there's a lot of action. I just kind of go with the flow in these games," said Saros, who is 8-1-0 in his past nine starts.
Brown scored on a breakaway at 9:37 to cut the lead to 3-1. He had not played since Dec. 19 at the Washington Capitals, missing three games in NHL COVID-19 protocol.
Frk made it 3-2 at 10:33 of the third period, scoring on a half-slap shot from the right point through traffic. It was his first goal since March 11, 2020.
"Let's face it, he did what we asked him to do coming up here, shoot the puck in the net," Kings coach Todd McLellan said. "He was the one guy that finished on the power play. Good for him. He's not afraid to shoot it."