Philadelphia has lost in each of its last 11 trips to New Jersey.
The Flyers failed to score for just the second time this season and had a three-game winning streak snapped.
Brodeur, who has 96 career shutouts, has held Philadelphia scoreless eight times.
Elias scored after missing the two previous games with a groin injury. His goal was the last of the game and came with 7:15 remaining in the second period.
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