Alex Stalock made 32 saves for Minnesota (37-35-9), which was shut out for the 10th time this season and seventh time at home.
"It's very frustrating. I was getting mad on the bench saying, 'We aren't getting shut out again,'" Wild coach Bruce Boudreau said. "You can't win like that."
Joakim Nordstrom gave the Bruins a 1-0 lead at 8:21 of the second period, shooting into an open net after Noel Acciari poked the loose puck to him after Matt Grzelcyk's initial shot went wide.
David Pastrnak extended the lead to 2-0 at 17:51 of the third period, and Senyshyn scored an empty-net goal 36 seconds later for the 3-0 final.
"[30 years from now I'll say the goal was] top-shelf, dangled a couple guys before. No, again, it's a dream come true anyway you put it," Sensyshyn said. "Put the puck in the net in the National Hockey League, you're never going to forget it.