The Bruins won the Eastern Conference finals 4-0 and held the high-scoring Penguins to just two goals in the stunning sweep.
Boston will face either the Chicago Blackhawks or Los Angeles Kings when the Bruins shoot for their second Stanley Cup title in three years.
Chicago leads that series 3-1 and can advance to the finals with a home win on Saturday night.
The Penguins’ season ended swiftly and shockingly. The NHL’s highest scoring team got zero points in the series from offensive stars Sidney Crosby and Evgeni Malkin.
McQuaid scored at 5:01 of the final period on a 45-foot slap shot from the right over the glove of goalie Tomas Vokoun.
That unleashed loud chants of “We want the Cup!” from the capacity crowd.
The top-seeded Penguins were trying to overcome both the disciplined defense of the fourth-seeded Bruins and history. Only three teams had lost a series after winning the first three games. The last was the Bruins in the 2010 Eastern Conference semifinals against the Philadelphia Flyers.
Pittsburgh was swept for the first time in 47 series. The last team to do it was Boston in 1979.