Reserve winger Ken Solheim, who has played in just 26 games this season, made a slap shot with 1:55 to play and gave Minnesota its fourth straight Boston Garden victory since its 34 consecutive winless visits there.
This was the North Stars' 12th victory in 17 games.
Solheim broke in on the left wing, took a pass from Kent-Erik Andersson and sent a 30-footer deflecting off the pad of goalie Marco Baron and into the net. It was Solheim's fourth goal of the season and his second game-winner.
The Bruins, who trailed only once before Solheim's winner, had tied at 5-5 at 10:42 of the third period on a goal by Terry O'Reilly, back from a nine-game absence with a shoulder injury.
Keith Crowder, Wayne Cashman, Peter McNab and Rick Middleton had the other Bruin goals. Middleton's was his 49th, putting him one shy of becoming the first Bruin to score 50 in a season since 1975.
Two North Star goals went in off Boston players. Steve Payne was credited with a second-period goal that tied the game at 3; it went in off Middleton's stick in a clearing attempt. Jack Carlson received credit for the goal that gave Minnesota a 5-4 lead when his backhander deflected in off the stick of Brad Park