Flames veteran Michael Cammalleri was the only shooter on either team to score a goal in the shootout as the Flames won their second consecutive game.
Karri Ramo is now 2-0 for the Flames since missing 15 regular season games with a knee injury. Ramo, who made 25 saves in a 8-1 win over Edmonton on Saturday, made 34 saves against the Sharks.
Joe Colbourne tied the game for the Flames in the second period after James Sheppard opened the scoring for San Jose with 1:49 left in the first period.
The Flames' victory was a surprise because the Sharks are 34 points ahead of the Flames in the Western Conference standings.
Calgary's next game will be against another formidable Western Conference opponent, the Anaheim Ducks on Wednesday. The Ducks at 99 points, are only two points back of the Sharks.