Elias started his four-point night by recording an assist with Paul Martin on Brian Gionta's ninth goal this season just 40 seconds into the first period. Later, he assisted on Johnny Oduya's power-play goal, also in the first, and added his own power-play tallies in the second and third periods.
Elias extended his point streak to nine straight games.
Travis Zajac had a goal and an assist. Zach Parise had four assists, while Scott Clemmensen made 24 saves on 25 shots in the opener of the Devils' four-game homestand.
Ottawa averted a shutout when Jarkko Ruutu scored shorthanded at 8:37 of the second period.
Alex Auld was beaten five times on 26 shots in the Senators' fifth loss in six games.