The Devils won for the eighth time in 11 games and reached 20 wins for the season.
Sykora produced the only first-period goal and then scored 1:26 into the second. Zach Parise boosted the lead to 3-0 with a goal at 6:55 of the second, assisted by Mark Fayne and Adam Henrique.
Thomas Vanek put the only shot past Brodeur 7:41 into the middle period, preventing the 19-year veteran goaltender from earning what would have been his first shutout of the season.
Brodeur raised the NHL's all-time record victory total to 635. Ryan Miller took the loss while stopping 20-of-23 shots.