Anton Forsberg made his third straight start for the Sens (7-15-1) and stopped 22 shots while Drake Batherson and Brady Tkachuk had goals. Mackenzie Blackwood turned away 23 shots for the Devils (9-9-5) as Damon Severson and Nathan Bastian scored.
"We trailed twice and stayed with it," Sens head coach D.J. Smith said. "We stayed disciplined and played within our systems.
"You can see some confidence … we know what we have to do to win games."
In the shootout, Josh Norris and Tim Stützle scored while Forsberg stopped two of three shooters to secure his third straight victory.
"It's funny how things can change super quickly," Norris said. "You put together a good game, and then you feel good. Then you put together another one and you just start to roll so we're definitely looking to keep this going."
New Jersey needed just 35 seconds to open the scoring and it came on Severson's third of the year as his point shot from the blue line evaded traffic and beat Forsberg for a 1-0 lead. Their lead was nearly doubled as on a partial breakaway Pavel Zacha hit the post just past the mid-point of the period.
The Sens thought they had the tying goal 5:15 into the second period as Nick Holden drove the net and saw his shot saved before Connor Brown scored into the empty net on the rebound but it was determined that the Senators d-man had interfered with Blackwood as he fell in the crease.
Batherson did get the Sens level exactly two minutes later as from the left dot, he took a Thomas Chabot pass and fired a wrister high past Blackwood for his eighth of the year.
It wasn't tied for long, however, as Bastian tipped a P.K. Subban point shot home at 8:20 to give the hosts a 2-1 lead.
Once again though, the Sens came back to find the equalizer and this time it came through the captain as after Dougie Hamilton couldn't clear, Holden sent the puck in deep to Batherson who fed Tkachuk in the slot from behind the net for his eighth of the season at 12:42.
"We have that confidence that we can come back in the game," Batherson said. "We got a couple of goals to get us back in it and anything can happen in overtime and the shootout so we're happy we came out on top."
In the third period, Jack Hughes hit the post with just over 12 minutes to play while in overtime, there were no whistles as the game flew right to a shootout, with Brown coming the closest for the Sens with an effort from the slot that was denied by Blackwood.
"The boys made a few nice moves in the shootout and Forsberg made some big saves," Batherson said. "Three in a row now and I think we're playing good hockey."
With an assist on Tkachuk's goal, Holden recorded the 100th of his career.
With two points tonight, Tkachuk tallied his 33rd career multi-point game. The only players that have recorded more with the Senators before age 23 are Martin Havlat (56), Marian Hossa (47), Alexei Yashin (46), Jason Spezza (44), Erik Karlsson (40) and Alexandre Daigle (40).
Ottawa is back in action Tuesday when they return home to host the New York Islanders.
