Jagr's power-play goal in the second period, which gave New Jersey a 3-0 lead, was the 693rd of his career. That moved him into eighth place on the NHL's all-time list ahead of Steve Yzerman.
Stephen Gionta's shorthanded goal just 2:02 into the game started the New Jersey assault and Reid Boucher added a first-period score.
Damien Brunner and Eric Gelinas also tallied for the Devils, who defeated the Senators for the first time in five tries.
The win went to Martin Brodeur, who made 23 saves. Brodeur moved within 21 regular-season victories of reaching the 700 mark in his record-breaking career. He was coming off his 124th shutout, which he turned in against Tampa Bay last Saturday.
Robin Lehner took the loss while stopping 28 shots.