The Devils (16-7-4) moved past the Blue Jackets (17-10-1) to the top of the Metropolitan Division standings.
Travis Zajac scored his first goal of the season in the first period, Jesper Bratt added a third-period goal, and Nico Hischier collected two assists for the Devils on the final leg of a 2-1-0 road trip.
Nick Foligno scored for the Blue Jackets. Oliver Bjorkstrand and Seth Jones picked up assists.
The Blue Jackets had a five-game home winning streak ended and dropped their second game in a row overall. Sergei Bobrovsky was in goal for both losses. He had 32 saves against the Devils.
Cory Schneider finished with 41 saves for the Devils.
Hall broke a 1-1 tie at 4:47 of the second period with his ninth goal of the season before Noesen gave New Jersey a two-goal lead with his second of the season.
Noesen reached into the crease after a shot trickled behind Bobrovsky with 45.1 seconds remaining in the second period just after a New Jersey power play ended.
Hall, who also had an assist, leads the Devils with 29 points this season.
Zajac's goal at 4:24 of the first period opened the scoring. Foligno was unable to clear the puck, and Zajac pounded on the puck, beating Bobrovsky.
Foligno came back and tied the score at 13:46 of the first. Parked in front of the crease, Foligno deflected a shot from just above the left circle from Bjorkstrand past Schneider.
The Blue Jackets' first goal came just after a power play ended. The league's worst power play with only seven goals this season was unable to convert on six chances in the game.
NOTES: The Devils and Blue Jackets play the second game of a home-and-home series Friday night at New Jersey. ... D Steven Santini, scratched in the past two games, replaced D Ben Lovejoy in the Devils' lineup. ... Blue Jackets LW Sonny Milano was sent to Cleveland of the American Hockey League because of a rosters numbers issue after LW Matt Calvert returned from the injury list. Milano has five goals and 10 points in 24 games for Columbus this season. "Sonny will be back. He's going to be part of his team," Blue Jackets coach John Tortorella said. ... Dale Earnhardt Jr., the recently retired NASCAR driver, dropped the ceremonial first puck.