Backstrom was perfect in the third period as Boston outshot the Wild 22-3, hanging on to record his fourth shutout of the season and 26th of his career.
Chad Rau and Matt Cullen scored in the second period for Minnesota, which managed to avoid a franchise-record eighth straight loss even without leading playmaker Mikko Koivu, who missed a second consecutive game with an undisclosed injury.
Tim Thomas stopped 27-of-29 shots for the Northeast Division-leading Bruins, who dropped to 1-2-0 on a six-game road trip.
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