Mark Giordano and Jarome Iginla each had a goal and an assist for the Flames, who have lost two in a row and six of seven overall. Jay Bouwmeester also scored for Calgary, which got 31 saves from Miikka Kiprusoff.
The Sharks drew first blood at the 1:06 mark of the first period. Thornton's wrister from the left circle on the power play got past Kiprusoff.
Clowe added a wrist shot from the left circle at the 10:24 mark to give San Jose a 2-0 lead.
Giordano put Calgary on the board with a power-play goal just 51 seconds into the second. The Sharks, though, got the goal back with 3:38 remaining when Pavelski jammed home a rebound.
Bouwmeester lit the lamp at the 9:14 mark of the third to cut the gap to 3-2.
The Sharks scored with 5:50 left to take a 4-2 lead. Clowe led a 2-on-1 rush down the right side of the ice before dishing off to Couture, whose wrister beat Kiprusoff.
Iginla's one-timer from the left circle cut the deficit to one, 4-3, with 37 seconds left.
The Flames beat the Sharks, 4-0, in Calgary on October 24...Calgary went 1- for-7 with the man advantage, while San Jose went 1-for-5 on the power play.