Chris Kunitz started Pittsburgh's third-period surge with his 18th goal of the season and Sutter beat Boston's Anton Khudobin twice in less than four minutes, including the game-winner with 2:03 remaining.
Marc-Andre Fleury stopped 14 shots for the Penguins, who broke loose late against the NHL's best defensive team.
Zdeno Chara and Tyler Seguin scored first-period goals for the Bruins. Khudobin made 31 saves and the Bruins kept Pittsburgh's high-powered offence in check until the final minutes of a matchup between two of the Eastern Conference's best teams.
There's no discouragement in that room. There's no issues there at all to be honest with you. It's more about, 'Hey, it's opportunities for players.' And if we become that bad of a team because of one player, it's not a real good sign for our hockey club. So this is part of sports. It's part of hockey.
— Bruins coach Claude Julien on the loss of Zdeno Chara to injury