Max Jones scored, and Ryan Miller made 30 saves for the Ducks (8-15-6), who lost 6-0 to the Sharks on Friday and are 2-9-3 in their past 14 games without a win in regulation.
"We were better than last game, but still not good enough," Ducks coach Dallas Eakins said. "We've got to, to a man, be harder to play against. We've got to treat that puck like it's our wallet. If somebody comes up to you on the street trying to take your wallet, I'm pretty sure they're going to be in for a rough time."
Eakins said the team held a meeting Saturday morning following the one-sided loss on Friday, which was the first time Anaheim was shut out this season.
"Our whole group should be frustrated," Eakins said. "If you're just walking in here every day like this is all rainbows and butterflies, that's not a very good attitude to have, so there has to be frustration. But you've got to channel that in the right direction, and not one that turns into the frustration of, 'Poor me,' or pointing a finger at somebody else. Your frustration has to drive you to be better and to be harder."
San Jose scored on its first shot of the game two seconds after an Anaheim power play ended for a 1-0 lead at 6:16 of the first period.
Ducks defenseman Ben Hutton overskated a pass coming through the slot. Kane retrieved the puck and headed the other way on an odd-man rush, scoring with a wrist shot from the left circle.
Kane has 13 points (seven goals, six assists) in the past 10 games.
The Sharks didn't take another shot on goal until 11:10 of the first period, but the only two shots on goal for the Ducks in the first 10:24 were clears from the other side of the red line on the penalty kill.