Andreas Engqvist scored in the first for Montreal (2-2), and Alex Auld, who faced one shot in the second, made 11 saves.
Kyle Brodziak scored Minnesota's second goal of the third with 13 seconds remaining to cut the lead to one. Cal Clutterbuck and Justin Falk also scored for the Wild (0-3-1).
Anton Khudobin stopped 24 shots for Minnesota, which was outshot 28-14 overall, including 13-4 in the first and 9-1 in the second.
Khudobin is bidding to back up No. 1 goalie Niklas Backstrom. Josh Harding is out indefinitely after tearing knee ligaments on Friday in St. Louis.
Montreal took a 2-1 lead 6:23 into the second when Alexandre Picard's shot from the left point struck White on its way past Khudobin.
Boyd made it 3-1 with the Canadiens' next shot at 6:57 after he stripped the puck from Wild defenseman Clayton Stoner.
Nash drove Montreal's 18th shot past Khudobin from the left faceoff circle at 8:02. The Canadiens scored three times on three shots in a span of 1:39.
Engvist opened the scoring 9:49 with Montreal enjoying a 12-1 margin in shots.
Clutterbuck drew Minnesota even at 1 on the Wild's second shot 12:12 in. Falk made it 4-2 in the third.