Nino Niederreiter and Dany Heatley scored for the Wild, who had a four-game winning streak end.
It was the second regulation loss for the Wild in their past 14 games and snapped an eight-game point streak which was their best since a 10-game point streak March 8-27, 2007 (9-0-1).
Minnesota completes a back-to-back road set against the Ottawa Senators on Wednesday.
Wild goalie Josh Harding was chased from the game after Pacioretty scored his third goal. Harding, named one of the NHL's Three Stars of the Week on Monday after going 3-0-0 with a 1.38 goals-against average and a .936 save percentage, was replaced by Darcy Kuemper. Harding finished with 16 saves on 19 shots; Kuemper allowed three goals on nine shots.
Montreal had scored three goals in three games coming into Tuesday, so coach Michel Therrien switched his forward lines, and they clicked.
Montreal outshot Minnesota 9-7 in the first period with the best chance coming on a Harding glove save off Pacioretty. But the Canadiens seemed to feed of their early chances and Pacioretty would score three straight goals in the second period.
Bournival added a goal in the second period, and Briere and Galchenyuk scored in the third for Montreal, which led 5-0.
Montreal's power play at Bell Centre was 8-for-45 (17.8 percent) but the Canadiens went 2-for-5 on the man-advantage with goals from Pacioretty and Galchenyuk.
The Canadiens play at the Washington Capitals on Friday in the first half of a back-to-back which sees them return home to face the Pittsburgh Penguins.