Ridly Greig tied it 2-2 on a wrist shot from the slot at 4:06, and Angus Crookshank, playing his first game since Jan. 4, scored on a one-timer from the right circle for a 3-2 lead at 6:02.
"I scored a couple times like that (in the American Hockey League), but it's just one of those shots where you don't really feel the puck off the blade, and normally, those kinds of shots have a funny way of finding the back of the net," Crookshank said.
Chabot pushed it to 4-2 at 9:01 on a snap shot at the left post after a pass from Tkachuk.
"I think up two goals, we knew they were going to come and some of their top guys were going to try and cheat a little bit behind us," Chabot said. "I think everybody did a great job keeping the player in front of them, not forcing anything, and obviously, that led to a lot more scoring chances."
Drake Batherson went top shelf on a backhand from the slot at 10:15 of the third period for the 5-2 final.
NOTES: The Senators scored five goals on the road for the fifth time this season. They've scored more goals as the visiting team once (6-3 win at the Toronto Maple Leafs on Nov. 8). ... The goals by Bratt and Nosek were the fifth-fastest to start a period in Devils franchise history. ... New Jersey defenseman John Marino played 20:44 in his return after missing two games with an upper-body injury.