San Jose was protecting a 2-1 lead and trying to kill a high-sticking penalty on Marcus Ragnarsson when Anaheim defenseman Oleg Tverdovsky could not control the puck at the left point.
Sturm skated over and got the puck in the neutral zone to begin a breakaway that he finished by tucking a wrist shot behind goaltender Steve Shields for his seventh goal just 70 seconds into the second period. Sturm also had a shorthanded goal in San Jose's 4-2 win at Anaheim on Oct. 31.
Teemu Selanne and Damphousse also had a goal and an assist as the Sharks improved to 2-1-1-1 on their current six-game road trip.
Selanne opened the scoring with his fourth goal of the season just 78 seconds into the contest. Since coming to San Jose for Shields and Jeff Friesen on March 5, Selanne has four goals and three assists in four wins over the Mighty Ducks.
San Jose goaltender Evgeni Nabokov made 27 saves and improved to 8-5-3.