The Bruins chased Luongo at 8:35 after Andrew Ference's power-play goal made the score 3-0. Luongo had previously allowed goals 35 seconds apart by Brad Marchand and Milan Lucic.
Vancouver coach Alain Vigneault made the decision to pull Luongo after he stopped five of eight shots.
Backup Cory Schneider replaced Luongo and gave up another goal in short order and the Canucks trailed 4-0 after 20 minutes.
Luongo and Boston goaltender Tim Thomas had done some verbal jostling prior to the game.
After the Canucks won 1-0 in Game 5 Friday, Luongo said he probably could have stopped the winning goal.
"It's not hard if you're playing in the paint, so it's an easy save for me,'' Luongo said. "But if you're wandering out and aggressive like he does, that's going to happen.''
Later, Luongo tried to backtrack a little, but still sent a zinger at Thomas.
"I said also he might make some saves that I don't,'' said Luongo. ''I was just saying, on that particular play, I would have played it different. That's the difference between me and him.
''I have been pumping his tires ever since the series started. I haven't heard one nice thing he had to say about me. That's the way it is.''
Thomas fired back at Luongo.
"I guess I didn't realize my job was to pump up his tires," said Thomas. "I guess I have to apologize for that."
Luongo has allowed just two goals against the Bruins in three games in Vancouver and has two shutouts. But he has given up 15 goals in three games in Boston.
Both Luongo and Thomas are finalists for the Vezina Trophy, awarded to the NHL's top goaltender.
The tall, lanky Luongo plays a conventional butterfly style. He uses his size and quick movements to block shots.
The stocky Thomas, nicknamed The Tank, is more unorthodox. He challenges shooters, looks to be out of position, then scrambles back to make saves.