Marian Stastny had two goals and three assists and Real Cloutier scored three goals to lead Quebec at home.
Stastny got both of his goals in the second period when the teams combined for 10 goals.
"It was a rout and I don't want to talk about it," Coach Gerry Cheevers of the Bruins said. "The Nordiques were the the instigators all night. We didn't hit a soul.
"We can't outskate or outscore Quebec in this type of game. We didn't attack or force the play."
Andre Dupont opened the scoring at 1:50 of the first period with a backhander. Cloutier's power-play goal made it 2-0, but Boston's Mike Krushelnyski cut it to 2-1 to end the first-period scoring.
In the second period, the Bruins hit the post twice before Rick Middleton tied it at 1:29.
Quebec replied with four straight goals before the period was half over. Peter Stastny scored his 21st and Marc Tardif got a goal less than one minute later. Marian Stastny raised Quebec's lead at 8:27, converting a goal-mouth pass from Peter for his 21st of the year. The Bruins then replaced goaltender Pete Peeters with Mike Moffatt.
Less than a minute later, Cloutier greeted Moffat with his 12th goal.
Marian Stastny was charitable toward the Bruins.
"The Bruins looked a little tired," said the eldest Stastny. "They've had a hard schedule lately and weren't checking as well as they can."