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.
You know what? We've played in some pretty special buildings along this playoff run so far. You start in Detroit, you go to Montreal, you come here … I think it's the first team to beat three Original Six teams to get to the Final if I'm not mistaken. That says how tough the road has been. Those are tough places to win.
— Lightning forward Steven Stamkos after Game 7 win vs. Rangers on Friday in New York