Benn Ferriero scored the only goal of the game to end the Sharks' three-game losing streak.
The loss spoiled a solid night by Calgary goaltender Miikka Kiprusoff, who stopped 26-of-25 shots but could not prevent the puck from crossing the goal line during a scrum in front of the net at 11:35 of the third period.
The Flames saw their two-game win streak come to a halt.
A total of just five penalties were called in the game, two of which were offsetting calls late in the third period.
Celebrity Families of 2014 [PHOTOS]