Alex Iafallo scored his first NHL goal for the Kings (10-2-2), who have earned a point in all seven home games but failed to win their fifth straight at Staples Center. Alec Martinez and Christian Folin also scored, and Darcy Kuemper made 27 saves.
The Predators jumped out to a 3-0 lead, but the Kings responded with three goals in the third period.
"I guess at the end of the day you'd be happy with the point, because it didn't look like we were going to get one. But I feel I don't like losing, so overtime or regulation, (it's) not much fun," Kings coach John Stevens said.
Iafallo scored 16 seconds into the third period to start the Kings rally.
Folin made it 3-2 at 5:20 of the third after baiting Saros into thinking he was going to dump the puck in off a faceoff. When Saros started to head behind his own net, Folin shot into the open goal from one step inside the red line for his first goal with the Kings.