The Wild trailed 3-2 heading into the final period but Chuck Kobasew tied it 5:14 into the stanza and Brent Burns gave Minnesota the lead with 10:45 to go. Brodziak put a backhander past Antero Niittymaki 1:20 later for insurance.
Brodziak opened the scoring on the power play 7:08 into the contest on Minnesota's first shot of the game and ran his goal total for the season to eight.
Minnesota won for the fourth time in six games. Niklas Backstrom got the victory with 29 saves.
San Jose has dropped two in a row after a four-game winning streak. Niittymaki allowed all five goals on 24 shots.
Brodziak produced two goals in a game for the third time this year.