Patrik Laine scored and Laurent Brossoit made 23 saves for the Jets (25-23-4), extending their season-long losing streak to five games.
"We'll go right through that game, because there's too many good things for us not to recognize that that's a game you can win with," Winnipeg coach Paul Maurice said. "Our offensive game was right, pucks to the net, a better mentality there. Good fight, good heart, good bench. I'm proud of the way our hockey team played tonight."
Laine gave the Jets a 1-0 lead at 6:06 of the first period.
"I think we played a good game against one of the best teams in the League," Laine said. "I think that's the way we need to play, [we] just don't get the results sometimes. Got to stay with it. Got to stick to the grind. Hopefully, it will turn if we work hard."
Bergeron tied it 1-1 on a 5-on-3 power play with 53 seconds remaining in the first period. DeBrusk put the Bruins ahead 2-1 on the power play at 3:07 of the third period.
"I knew it was coming to me, so I just tried to keep my stick down, because I know I've missed about 500 of those," DeBrusk said. "I've missed a lot of those this year, so I was just trying to bear down on my stick and try to put it in, maybe catch him going side to side."