The Wild are 4-0 all-time in Boston and have only lost to the Bruins once in seven games. Brian Rolston scored his team-leading 27th goal to give Minnesota a 1-0 lead 3:59 into the second period when he wristed a shot over the shoulder of Bruins goalie Tim Thomas.
Bouchard doubled the lead for the Wild when he converted a breakaway and slid the puck through Thomas' legs with seven minutes remaining in the second.
Brandon Bochenski cut the deficit to 2-1 with 1:36 remaining in the game when he re-directed a shot by Dennis Wideman past Backstrom.
The Bruins lost consecutive home games after a previously successful weekend beating arch-rival Montreal followed by a road win over New Jersey.