Dustin Brown scored two goals and had an assist for the Kings (3-6-3), who lost their fifth straight game despite taking the lead after falling behind by two goals. Cal Petersen made 37 saves.
San Jose forward Patrick Marleau played his 1,734th game to pass Jaromir Jagr for third in NHL history. The 41-year-old needs 23 games to move ahead of Mark Messier (1,756) for second and 34 to pass Gordie Howe (1,767) for first.
"I thought he was unreal tonight, I thought he played his best game of the year," Couture said. "He can still skate. He can probably play until he's 65 and still be able to skate in the NHL."
Brown gave the Kings a 3-2 lead at 10:45 of the third period on a wrist shot from the right face-off circle, but Kane tied it when he jammed a rebound into an open net at 19:15 with Jones pulled for an extra attacker.
"'Kaner' has been pretty good the last few games, and it's nice to see him where he's getting that goal from," Sharks coach Bob Boughner said. "Digging around the blue paint, I think that's his game, and he's a big body and tough to move out of there. He did an excellent job with a timely goal."
Kopitar scored on a breakaway to get the Kings within 2-1 at 7:00 of the second period. Brown tied it 2-2 at 17:54 when he put in the rebound of Adrian Kempe's shot on the power play.