Minnesota won its third in a row and increased its Western Conference-leading point total to 35.
Zach Parise gave the Devils the early lead by scoring on a slap shot 2:54 into the contest. The Wild then ran off three unanswered goals to move in front.
Dany Heatley scored a mere 20 seconds after Parise's tally and Brodziak gave Minnesota the lead 3:41 later with the first of his two goals in the game. Casey Wellman finished off the first-period surge by scoring his first goal of the season and his third in 29 NHL games scattered over three years.
Ilya Kovalchuk brought New Jersey within one late in the first period and Minnesota held onto its 3-2 lead until Brodziak added some insurance with 3:36 to go in regulation.