Brown made it 4-1 at 19:52 with his ninth power-play goal.
"I feel like most nights we're getting a lot of chances," Athanasiou said. "We just had some real unlucky bounces and unfortunate puck luck, but today it kind of worked out and the chances we did get we just capitalized on them, so that was a good feeling."
Meier scored 14 seconds into a power play, pulling the Sharks within 4-2 at 12:31 of the third period.
Carter put the Kings ahead 1-0 at 11:43 of the first period, jamming in the rebound of Mikey Anderson's shot from the point that had been redirected by Athanasiou.
Gambrell scored for the second straight game to tie it 1-1 at 16:54. Quick thought he had covered up Christian Jaros' shot that had been tipped by John Leonard, but Gambrell chipped in the loose puck. He has three goals in his past four games.
"We had chances early on in the game, being up on the power play to sort of cement a lead. We didn't, and they got better as the game went on and we went the other way," Boughner said.
NOTES:Kings defenseman Olli Maatta had an assist and blocked three shots in 19:10 after missing nine games with an upper-body injury. … Los Angeles forward Blake Lizotte played his 100th NHL game. … Gambrell has five goals in 36 games, matching his total last season in 50 games. … San Jose was 2-for-22 (9.0 percent) on the power play in eight games against Los Angeles but won the season series 6-2-0. … The Sharks acquired defenseman Greg Pateryn and a fifth-round pick in the 2021 NHL Draft in a trade with the Colorado Avalanche for goalie Devan Dubnyk on Saturday.