Jarome Iginla scored twice, while Reilly Smith and Loui Eriksson also scored for the Bruins, who have ripped off nine wins in a row and now hold a five- point lead over Pittsburgh for the top spot in the Eastern Conference.
It is Boston's longest winning streak since a 10-game span from Nov. 1-23, 2011.
Jason Pominville scored the only goal of the game for the Wild, who have dropped five of their last six games. Darcy Kuemper gave up three goals on 28 shots in the loss.
After a scoreless first period, Boston took a 1-0 lead 3:52 into the second as Iginla flew in down the left side and fired a shot on net that was deflected by the defender, bounced in front of Kuemper and went between his pads.
It was a 2-0 lead for the Bruins eight minutes later when Carl Soderberg skated around the net from right to left and fired a backhand pass the other way where Eriksson potted his eighth of the year.
Minnesota made it a 2-1 game with 1:26 to play in the second as Ryan Suter's diving clear went to the middle of the ice where Pominville caught up to the puck and slapped it in from down low, breaking his stick in the process, for his 26th goal of the season.
Boston, though, got the goal back at 7:50 of the third as Patrice Bergeron's turnaround shot from the left circle was stopped, but the rebound came out to the right and Smith slammed it home.
Minnesota pulled Kuemper with 2 1/2 minutes to play, and Iginla sealed the win with an empty-netter and 1:05 showing on the clock.