Anze Kopitar and Nicholas Shore scored for the Kings (24-14-5), who have lost three straight. Jonathan Quick made 18 saves and has allowed 11 goals in his three straight regulation losses.
"I thought we had a lot of guys that showed up ready for the physical challenge, we had some guys that didn't and it cost us, so that's a good lesson for us," Los Angeles coach John Stevens told its website. "We cannot win in a game like that unless we have everybody, and we needed more tonight."
Kase scored at 2:10 of the third period to make it 3-0. Nick Ritchie stole the puck from Quick after he misplayed it behind his net and passed to Kase, who scored from the slot for his first NHL three-point game and second multigoal game.
Gibson lost his shutout with 11:28 remaining when Shore awkwardly struck Christian Folin's pass and the puck fluttered into the net to make it 3-1. Kopitar scored with 6:14 remaining to make it 3-2, and Perry scored an empty-net goal with 1:28 left for a 4-2 lead.
Kase threw a sharp-angle shot on net that caught Quick by surprise and snuck past him at 6:14 of the first period for a 1-0 lead. Kesler's goal on a wrist shot from the right dot with 1:10 left made it 2-0.
"It's tough. You play Anaheim, you obviously want to win those games that are a huge rivalry," Kings forward Alex Iafallo said. "We've got to have a good start. It all started in the first period, and the next game we've got to play all three periods."