Chicago leads that series 3-1 and can advance to the finals with a home win on Saturday night. If the Blackhawks get there, it will set up the first finals matchup of Original Six NHL franchises since 1979.
The Penguins' season ended swiftly and shockingly as the league's highest-scoring team got no 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, which never led in any of the four games against the Bruins, was swept for the first time in 47 series. The last team to do it to the Penguins was Boston in 1979.
The Penguins also lost the first three games of their opening-round series last year against Philadelphia before being eliminated in six games.
Rask was solid again with 26 saves, but didn't have to stop many challenging shots. His last save came with his glove at the final buzzer on Matt Niskanen's shot from 40 feet.
The Penguins had been shut out just twice in their previous 147 games before being blanked twice in the four games against the Bruins.
• Boston 1, Pittsburgh 0
Bruins win series 4-0
• Los Angeles at Chicago, 6 p.m., Ch. 5
Blackhawks lead series 3-1