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Dan Boyle also scored for San Jose, and Joe Thornton had two assists. The Sharks, 5-1-1 in their last seven, reached 50 wins for the second time in franchise history and moved four points ahead of Detroit in the race for the Presidents' Trophy.
Jarome Iginla got his 32nd goal of the season for Calgary late in the first period.
The Flames have lost eight of their last 12 as their lead atop the Northwest Division has been cut to just one point over Vancouver. The Canucks have seven games remaining and Calgary has six.
San Jose took advantage of an early two-man advantage after Adrian Aucoin's clearing attempt went over the glass for an automatic delay of game penalty. Just 35 seconds later, Thornton found Boyle with a centering pass and Boyle fired a slap shot into the top corner to put the Sharks up 1-0 at 6:11 of the first period.
Iginla tied it with 4:51 left in the period, taking a pass from Daymond Langkow at the face-off dot and snapping a shot that Nabokov only got a portion of.
Cheechoo, back in the Sharks' injury-riddled lineup after missing two games with a lower body injury, then deflected Brad Lukowich's slap shot from the blue line past Miikka Kiprusoff with 7:36 left in the second with the game-winner.
Nabokov made the lead stand with 12 saves in the third period, including several clutch stops. His best save came on a power play midway through the period when, while sprawled on the ice, he reached back and was able to smother a shot from Mike Cammalleri.
Earlier in the period, Nabokov also made an alert glove save off Eric Nystrom and kicked out a pad to stop Adam Pardy from in-close.
Notes:@ San Jose LW Milan Michalek snapped a six-game points streak (three goals, four assists). ... San Jose has killed off 17-of-18 penalties over the last seven games. ... Calgary lost D Cory Sarich late in the third period when he took a slap shot from Thornton off his skate. He was noticeably favoring his right foot as he was helped off the ice and went straight to the Flames' dressing room.
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