Thomas Greiss had 24 saves for San Jose and stopped all four Los Angeles skaters in the shootout. He came close to starting the preseason with a shutout but Dustin Brown tied the game at 1 with 9.5 seconds left in regulation.
Demers went to the backhand to beat Jonathan Quick for the only goal of the shootout.
Benn Ferriero, a rookie who had 37 goals for Boston College last season, had the Sharks' goal in regulation.
The Kings (1-2) had been 0 for 7 on the power play before Sharks forward Dan Hinote was called for a high-sticking penalty with 20 seconds left in regulation. Brown corralled a pass from Teddy Purcell in front of the goal and calmly swiped the puck past Greiss to tie it.
The Sharks had two power-play chances in the overtime, but were shut down by a series of acrobatic saves by Quick, who stopped 22 shots.
Forward Dany Heatley - acquired in a trade with Ottawa on Saturday - also didn't play. Heatley will practice with the Sharks on Friday morning before participating in an introductory media session.