Goaltender Jamie Storr started the play when he caught the Sharks on a line change and passed to defenseman Jaroslav Modry, who worked the puck to Allison. Heinze circled around Allison, took a pass from his linemate, broke in alone and beat goaltender Evgeni Nabokov for his ninth goal.
Moments earlier, Storr stopped Alexander Korolyuk on a penalty shot after Korolyuk was taken down on a breakaway by defenseman Mattias Norstrom. Korolyuk faked right and went to his backhand, but his shot hit the goalpost.
Less than a minute later, Korolyuk hit the same post with a slap shot from outside the left faceoff circle.
Storr has stopped all three penalty shots taken against him and made 22 saves for his second win of the season and second in as many games.
Mikko Eloranta put the game out of reach with his first goal for the Kings. He got a pass from Craig Johnson at 8:04 and put a quick shot past Nabokov's glove.
Nabokov was replaced 53 seconds later by Finnish rookie Vesa Toskala.
Less than four minutes into the game, Allison staked the Kings to a 1-0 lead with his fifth goal in six games. Nabokov stopped a deflection by Modry, but Allison put in the rebound from the left side.
The Sharks tied it with 3:14 left in the second period on Teemu Selanne's power-play goal. Selanne was unchecked at the left point, took a cross-ice pass from rookie defenseman Jeff Jilsson and beat Storr between the pads with a wrist shot.
Selanne has 28 goals and 38 assists in 46 games against the Kings. But he could not prevent San Jose from suffering its fourth straight loss.
Swim Week Miami Beach 2014 [PHOTOS]