Shane Pinto, Stephen Halliday and Tyler Kleven scored for the Senators (5-1-0), who reached the five-win mark in six or fewer games for the third time in franchise history after previously doing so in 2007-08 (5-0-0) and 2005-06 (5-0-0). Linus Ullmark made 29 saves.
Ullmark (5-0-0) has allowed just six goals this season.
Arseny Gritsyuk scored the lone goal, and Nico Daws made 16 saves for the Devils (2-3-0), who won 4-1 against the Vancouver Canucks on Saturday.
Pinto gave the Senators a 1-0 lead nine seconds into the second period on a wrist shot from the slot, converting Michael Amadio's centering pass from the left face-off circle.
Halliday pushed it to 2-0 with a power-play goal at 8:40 of the second. Devils defenseman Brett Pesce hit an edge and fell, opening a lane for Stutzle to find an uncovered Halliday between the circles.
Stutzle made it 3-0 when he deflected a shot from the slot past Daws at 11:10 of the third period. Thomas Chabot took the initial shot from the point.
The Devils appeared to pull within 3-1 at 11:58 of the third when Jesper Boqvist scored, but the Senators successfully challenged the play for goalie interference.
Gritsyuk did cut the deficit to 3-1 at 14:59 on a wrist shot between the circles.
Kleven scored an empty-net goal at 17:53 for the 4-1 final.
New Jersey denied Ottawa on a five-minute major penalty against Anthony Mantha for boarding defenseman Nikolas Matinpalo at 10:01 of the first.
Matinpalo sustained an upper-body injury on the play and didn't return, limiting the Senators to five defensemen.
