Ryan Miller made 27 saves for the Ducks (31-36-10), who were playing the second game of a back-to-back and their third game in four nights.
"We're just trying to get every point, but this is more about the emotions going in and playing against this team," Ducks forward Rickard Rakell said. "We know that like, playoffs, we can't decide. Other teams have to lose, but obviously we're going into every game trying to get the two points and having a good feeling within the team down the stretch here."
Kopitar got Miller off-balance with a series of dekes before he reached back to his right and guided the puck around the goalie. Quick saved shots by Rakell and Jakob Silfverberg in the shootout.
"He did it the other direction two years ago," Miller said. "It's not impossible. It's just I should know better, honestly. I just didn't want him to get ahead of me on the blocker side. The last three or four shootouts he's had he's shot, so obviously he changed it up."
Grundstrom tied the game 3-3 at 16:07 of the third period with a tap-in at the far post off Tyler Toffoli's pass behind Miller and through the crease. It was his third goal in seven NHL games.
Carter Rowney put the Ducks ahead 3-2 at 9:42 of the third period with a shorthanded goal. Derek Grant stole the puck from Kopitar in the Kings zone and found a wide-open Rowney for his sixth goal.
The Kings went in front 2-1 at 13:48 of the second period when Jeff Carter scored with a sharp-angle wrist shot to Miller's short side, but the Ducks tied it 2-2 at 19:58 on Rakell's power-play goal when he put the rebound of Silfverberg's shot in under the crossbar with 1.1 seconds remaining.
"I knew there wasn't much time left," Rakell said. "As soon as [Silfverberg] shot the puck I thought it was going to be over quite soon after that, but then I saw the puck trickle down behind [Quick]. I just tried to get to it as quick as possible."
The Ducks took a 1-0 lead at 3:47 of the first period when Cam Fowler scored his fifth goal on a shot from the blue line through traffic.
Clifford tied it 1-1 at 5:09 when he got position in front of Miller and tipped Alec Martinez's long shot 16 seconds into a power play. It was Clifford's first NHL career point on special teams in 599 games.
"I think [Martinez] just made a good play, got the puck to the net and it went off me, went in," Clifford said. "That's all I got for you. Simple as that."
