Brodeur, who in his 17th season dominates the NHL goaltending record book, won for the third time in four starts after struggling in the early weeks of the season. He posted the 672nd regular-season win of his career and his 122nd shutout.
It was just the fourth win of the season for the Devils and came against the team with the second fewest points in the league.
Adam Henrique deflected a shot from Eric Gelinas past Ray Emery just 1:57 into the game and Brodeur had to settle for a one-goal advantage until the third period.
Cam Janssen finally gave the Devils some breathing room 3:01 into the final stanza and Jaromir Jagr added an empty-net goal with two seconds to play.
Emery stopped 23-of-25 shots in defeat.