Jack Hughes and Jonas Siegenthaler each had two assists for the Devils (37-32-2), who have won five of their past six. Jacob Markstrom made 16 saves.
Steven Stamkos and Reid Schaefer scored for the Predators (34-29-9), who had their season-high five-game winning streak end. Justus Annunen made 27 saves.
Hischier gave the Devils a 3-2 lead on the power play at 14:07 of the third period with a deflection of a shot from the left face-off circle by Hughes.
Timo Meier added an empty-net goal at 19:27 to make it a 4-2 final.
Bratt put the Devils ahead 1-0 at 18:02 of the first period with a deflection of a one-timer from the right circle by Hughes. Bratt has scored in five consecutive games and has 12 points (five goals, seven assists) in a seven-game point streak.
Hischier extended it to 2-0 at 9:13 of the second period when he got a piece of a wrist shot from the left circle from Bratt.
Schaefer cut it to 2-1 at 11:09, scoring on a breakaway off a pass from Fedor Svechkov.
Stamkos then tied it 2-2 just 1:51 later. Luke Evangelista forced a turnover by Hughes in the New Jersey zone, and Stamkos beat Markstrom with a backhand at 13:00.
