Trailing 2-1 early in the middle frame, Sturm intercepted a clearing pass by Colin White deep in the San Jose zone, quickly turned on net and flicked a backhander past Thomas Greiss.
Less than 2 minutes later, Tomas Fleischmann gave Florida the lead off another Sharks turnover and Jack Skille made it 4-2 when he picked off a San Jose clearing pass and scored while the Panthers were shorthanded.
Logan Couture scored twice and Greiss finished with 30 stops for San Jose.
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