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.
It's about enjoying the moment. It's pretty cool to get that many people together and that excited about hockey to the point they really want you to mess up. They've got a ton of red jerseys and you have to sit back and appreciate people love hockey that much and you are the one out there who gets to play the game. Just try and stick with that respect for the game and also the mentality that for me it's just about entering the fight and seeing how long I can stay in it.
— Canucks goaltender Ryan Miller on what he expects from the fans in Calgary for Game 6