Sturm was Boston's first skater during the shootout and, after Pittsburgh's Michel Ouellet shot wide, he stuffed a shot under goalie Marc-Andre Fleury's pads. Evgeni Malkin and Sergei Gonchar each missed for Pittsburgh to end it.
The Penguins played without star Sidney Crosby because of an injury for only the second time in his two-season career and appeared to badly miss him, going 0-for-8 on the power play until Mark Recchi scored the tying goal with 30 seconds remaining in the third on a backhander.
Recchi also scored Pittsburgh's first goal, late in the first period, before Boston scored three times in 4 1/2 minutes in the second.
Stanislav Chistov's first goal of the season tied it on a power play, and Sturm made it 2-1 slightly more than two minutes later. With Pittsburgh's Jarkko Ruutu off for a double minor for roughing and unsportsmanlike conduct, Zdeno Chara scored the Bruins' third goal in 4 1/2 minutes with a slap shot from the high slot after he and Patrice Bergeron exchanged passes.
The Bruins won their eighth in a row against Pittsburgh since 2003.
Malkin cut Boston's lead to one goal by scoring on a short breakaway midway into the third, stealing the puck from Brad Stuart along the boards and skating in alone for his 10th goal. Malkin nearly won it in overtime after swiping the puck in the Bruins' end, but goalie Tim Thomas stopped him by sticking out his right skate. Thomas made 16 saves after replacing Brian Finley following the first period.
Crosby, the NHL's fourth-leading scorer, injured his groin during a 5-3 victory in Philadelphia on Monday and had to watch from a private box. His status for games Friday and Saturday is uncertain.